Reformulation of Loop gravity in progress, comment?

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  • #101
Quite a lot of straight spin network stuff in Dittrich's Finite Groups paper (that the Escorial talk was based on, as you may have noticed.) It looks to me as if the way she uses "spin nets" they are not DUAL to spinfoam but rather, as she says, a dimensional reduction of spinfoams. Dittrich's pattern seems to be to explore variants, toy models, simplified (often lower dimensional) versions, to get a better understanding of the mathematics.

The finite group approach to spinfoam may (she suggests) serve a twofold purpose (1) as a way to get a better understanding of the usual continuous group case (2) as a way of facilitating calculations.
=================
To get back to the Tianjin conference.http://www.cim.nankai.edu.cn/activites/conferences/hy20120820/index.htm Finally I was able to get "Titles and Abstracts" link to work. These 14 talks may give us clues about what LQG will look like next July, when the Loops conference is held at Perimeter. Except for Yongge Ma the speakers are all young researchers, postdocs or junior faculty.
I have blue-lighted the talks of Dittrich and Engle, which are in areas I'm currently trying to understand better. Engle's talk is closely related to what several people in the Marseille group have been working on recently (geometric orientation, tetrad sign...). And Dittrich's talk is very much in the same vein as the papers we've just been looking at. I have also highlighted green the talks of Alesci, Bahr, Ding, Wieland and (at the end of the list) Zhang, primarily as a reminder to myself.


Session 8
Loop Quantum Gravity
Chair:
Jerzy Lewandowski (University of Warsaw, Poland)

Titles and Abstracts
Emanuele Alesci (University of Erlangen-Nürnberg, Germany)
Title: LQG Cosmology from the full LQG
Abstract: We present a new perspective on early cosmology based on Loop Quantum Gravity. We use projected spinnetworks, coherent states and spinfoam tecniques, to implement a quantum reduction of the full Kinematical Hilbert space of LQG, suitable to describe inhomogeneous cosmological models. Some preliminary results on the solutions of the Scalar constraint of the reduced theory are also presented.

Benjamin Bahr (University of Cambridge, UK)
Title: Spin Foam Models: Towards diffeomorphism-invariant path integral measures
Abstract: The aim of this talk is to describe how Spin Foam Models can be used to construct normalized Borel measure spaces that carry the action of a group of diffeomorphisms of a manifold Diff(M). These measure spaces can have the interpretation of a path integral for physical theories of connections, and in interesting cases the constructed measure is invariant under Diff(M). We outline the construction, give some easy examples, and comment on how the conditions for cylindrical consistency of measures corresponds to Wilsonian renormalization group flow equations. This construction could provide a framework for background-independent renormalization, which is in particular of interest for constructing a theory of quantum gravity.

Norbert Bodendorfer (University of Erlangen-Nuremberg, Germany)
Title: Towards loop quantum supergravity
Abstract: An introduction aimed at non-experts in loop quantum gravity will be given into the recently developed generalization of loop quantum gravity to higher dimensional supergravity. Possible applications will be discussed.

You Ding (Beijing Jiaotong University, China)
Title: The time-oriented boundary states and the Lorentzian-spinfoam correlation functions
Abstract: A time-oriented semiclassical boundary state is introduced to calculate the correlation function in the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam model. The resulting semiclassical correlation function is shown to match with the one in Regge calculus in a proper limit.

Bianca Dittrich (Perimeter Institute for Theoretical Physics, Canada)
Title: Coarse graining spin foam models: a tensor network approach
Abstract: Spin foams are microscopic models for quantum gravity and space time. We discuss coarse graining methods to extract large scale physics from these model and derive consistency conditions that these models should satisfy to be viable models of gravity.

Jonathan Engle (Florida Atlantic University, USA)
Title: Plebanski sectors, orientation, and spin-foams
Abstract: Spin-foams are a path integral quantization of gravity which, since several years now, remarkably has been shown to be compatible with canonical loop quantum gravity. Spin-foams start from the Plebanski formulation, in which gravity is recovered from a topological field theory, BF theory, by the imposition of constraints, called simplicity constraints. These constraints, however, select not just one gravitational sector, but two copies of the gravitational sector, as well as a degenerate sector. Furthermore, within each copy of the gravitational sector, two possible space-time orientations appear. In this talk, in addition to giving a brief introduction to spin-foams, we clarify the meaning of the different Plebanski sectors and orientations, show how one can remove the additional sectors, and discuss arguments in favor of doing so.

Marc Geiller (APC-University Paris 7, France)
Title: A three-dimensional Holst-Plebanski spin foam (toy) model
Abstract: We introduce an action for three-dimensional gravity that mimics key features of the four-dimensional Holst-Plebanski theory. In particular, the action admits an extension with Barbero-Immirzi parameter, and its canonical structure contains second class constraints. At the classical level, we discuss two variants of the canonical analysis, and study the properties of the three-dimensional Ashtekar-Barbero connection. Then we perform the spin foam quantization of the theory, and emphasize the role of the secondary second class constraints. Finally, we draw conclusions about the construction of four-dimensional spin foam models and more generally about the agreement between the canonical and covariant quantizations

Hal Haggard (Centre de Physique Theorique de Luminy, France)
Title: Pentahedral Volume, Chaos, and Quantum Gravity
Abstract: The space of convex polyhedra can be given a dynamical structure. Exploiting this dynamics we have performed a Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space, which is in excellent agreement with loop gravity. Here we present investigations of the volume of a 5-faced convex polyhedron. We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume. This results in new information about cylindrical consistency in loop gravity and a couple of surprises about polyhedra. In particular, we are interested in discovering whether the evolution generated by this volume is chaotic or integrable as this will impact the interpretation of the spin network basis in loop gravity.

Frank Hellmann (Albert Einstein Institute, Germany)
Title: Wave Front Set analysis of EPRL type Spin Foam models
Abstract: I show how to use tools from microlocal analysis in order to understand the asymptotic dynamics of spin foam models. Using these tools it is shown that the PRL model suffers a flatness problem, and how to modify the model in order to resolve this issue.

Wojciech Kaminski (Albert Einstein Institute, Germany)
Title: Coherent states and 6j symbols' asymptotics
Abstract: Coherent states proved to be useful both in defining spin foam models of Quantum Gravity as well as in deriving their asymptotic limits. The method of coherent states combined with stationary point analysis gives nice geometric interpretation of contributions to asymptotic expansion and dominating phase of each term. It is, however, very inefficient in providing full expansion due to problems with computation of the Hessian determinant. Even in the case of 6j symbols where Ponzano-Regge formula is well known, it was not obtained this way so far. By the slight modification of the method we circumvented the problem. We are able to prove conjectured alternating cos/sin form of the full asymptotic expansion, as well as derive different form of the next to leading order term. The latest can be obtained by a symmetric recursion relation similar to proposed by Bonzom-Livine but applicable to 6j symbol itself not its square. Our method works both in 3D euclidean and lorentzian case.

Marcin Kisielowski (University of Warsaw, Poland)
Title: Spin Foams contributing in first order of vertex expansion to the Dipole Cosmology transition amplitude
Abstract: In this talk we will present a general method for finding all foams with given boundary and given number of internal vertices. We will apply the method to the Dipole Cosmology model and find all spin foams contributing to the transition amplitude in first order of vertex expansion.

Yongge Ma (Beijing Normal University, China)
Title: Connection Dynamics of Scalar-Tensor Theories and Their Loop Quantization
Abstract: The successful background-independent quantization of loop quantum gravity (LQG) relies on the key observation that classical general relativity (GR) can be cast into the connection-dynamical formalism with the structure group of SU(2). Due to this particular formalism, LQG was generally considered as a quantization scheme that applies only to GR. Our work shows that the nonperturbative quantization procedure of LQG can be extended to a rather general class of 4-dimensional metric theories of gravity, which have received increased attention recently due to motivations coming form cosmology and astrophysics. I will introduce how to reformulate the 4-dimensional scalar-tensor theories of gravity, including f(R) theories, into connection-dynamical formalism with real SU(2) connections as configuration variables. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter Ω(φ). In the sector of Ω(φ)=-3/2, the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of Ω(φ)≠3/2, the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. Both sectors can be cast into connection dynamics by canonical transformations. Through the connection dynamical formalisms, I will further outline the nonpertubative canonical quantization of the scalar-tensor theories by extending the loop quantization scheme of GR.

Wolfgang Wieland (Universite de la Mediterranee (Marseille), France)
Title: The twistorial structure of spinfoam transistion amplitudes
Abstract: The EPRL spinfoam model is a proposal to define transition amplitudes for loop quantum gravity. Although its semiclassical properties are well understood little is known how the model can actually be derived from first principles. In this talk I will sketch a proof built upon the twistorial framework of loop quantum gravity. I will introduce a gauge-fixed integration measure on twistor space, study the quantum states on the boundary, solve the reality conditions, rewrite the classical action in terms of twistors, in order to then define a path integral. The integral can be performed explicitly, and reproduces the EPRL vertex amplitude. It fixes the face amplitude too, the correct form of which has always been a matter of debate. The formalism also allows to study the curvature tensor and to decompose it into its irreducible components, including the Weyl spinor and the torsion parts.

Mingyi Zhang (Aix-Marseille Universite, France)
Title: Asymptotic Behavior of Spinfoam Amplitude
Abstract: We give the detail analysis of the asymptotic behavior of EPRL spin foam model. The asymptotics of spin foam amplitude is totally controlled by its critical configurations. Using critical configurations we can reconstruct the classical geometry. We show that spin foam goes back to Palatini-Regge gravity when we take large spin limit.

I have highlighted the abstracts of Alesci, Bahr, Ding, Wieland, and Zhang as a reminder of topics to look into further.
 
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  • #102
marcus said:
It looks to me as if the way she uses "spin nets" they are not DUAL to spinfoam but rather, as she says, a dimensional reduction of spinfoams. Dittrich's pattern seems to be to explore variants, toy models, simplified (often lower dimensional) versions, to get a better understanding of the mathematics.

Yes, I read that too quickly. What's interesting to me is that there seems to be two different sorts of "renormalization" in tensor networks. MERA, which Physics Monkey has suggested is linked to AdS/CFT seems to me "wave function renormalization". The tensor network renormalization Dittrich is using seems more like "Hamiltonian" or "Action" renormalization.

I'd love to know if the two are related. I can only find a few comments, but the relationship seems formal. For example, Gu and Wen say cryptically "The tensor network renormalization approach is based on an observation that the space-time path integral of a quantum spin system or the partition function of a statistical system on lattice can be represented by a tensor trace over a tensor network ... We like to point out that in addition to use it to describe path integral or partition function, tensor network can also be used to describe many-body wave functions.".

I believe Dittrich and Gu and Wen are talking about related things, because both refer to Levin and Nave as the basis for tensor network renormalization. Ah, yes, they are the same thing, she cites Levin and Nave and Gu and Wen on slide 21 of http://www.ucm.es/info/giccucm/Escorial2011/Dittrich.pdf .
 
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  • #103
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  • #104
Incidentally at the science level, the organizers of Loops 2013 are Dittrich, Freidel, Smolin. It will be enlightening to see how they sort out the topics and evalutate directions in current Loop research, as they construct the program and arrange the plenary talks and parallel sessions.
http://www.perimeterinstitute.ca/en/Events/Loops_13/Loops_13/
Also I would suggest anyone who hasn't seen it check out Dittrich Freidel Smolin's listing of their International Advisory Committee at the Loops 13 webpage.
Since I haven't done this in a while, I'll update the list of potential reformulation topics I'm watching.

PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation.
http://www-library.desy.de/cgi-bin/spifaacce/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29
Ashtekar, Agullo, Nelson http://arxiv.org/abs/1209.1609 (A Quantum Gravity Extension of the Inflationary Scenario)
Ashtekar, Agullo, Nelson http://arxiv.org/abs/1204.1288 (Perturbations in loop quantum cosmology)
Artymowski, Dapor, Pawlowski http://arxiv.org/abs/1207.4353 (Inflation from non-minimally coupled scalar field in loop quantum cosmology)
By various of the following: Barrau, Grain, Cailleteau, Vidotto, Mielczarek
http://arxiv.org/abs/1206.6736 (Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology)
http://arxiv.org/abs/1206.1511 (Loop quantum cosmology in the cosmic microwave background)
http://arxiv.org/abs/1111.3535 (Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology)
http://arxiv.org/abs/1011.1811 (Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background)
http://arxiv.org/abs/1003.4660 (Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves)

Holonomy Spin Foam Models Spinfoam labels can be group elements. Finite groups are introduced. Some sample papers, some out, some in preparation:
Bahr, Dittrich,Hellmann, Kaminski http://arxiv.org/abs/1208.3388 (Holonomy Spin Foam Models: Definition and Coarse Graining)
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin foam models to arbitrary, in particular finite groups. The similarity with standard lattice gauge theories allows to apply standard coarse graining methods, which for finite groups can now be easily considered numerically. We will summarize other holonomy and spin network formulations of spin foams and group field theories and explain how the different representations arise through variable transformations in the partition function. A companion paper will provide a description of boundary Hilbert spaces as well as a canonical dynamic encoded in transfer operators.
[28] Same authors (Holonomy Spin Foam Models: Boundary Hilbert spaces and canonical dynamics, 2012, in prep) .
[29]Hellmann, Kaminski (Holonomy Spin Foam Models: Asymptotic dynamics of EPRL type models, 2012, in prep) .
For background, e.g. the transfer operator concept in spinfoam context:
Bahr, Dittrich, Ryan http://arxiv.org/abs/1103.6264 (Spin foam models with finite groups)
In what I think may be a related development Lewandowski's Warsaw group has a way to systematically ENUMERATE and compute spinfoam histories. They stack up successive spin network states of geometry and join them into a single history.
http://arxiv.org/abs/1107.5185

TwistorLQG Papers by Freidel, Livine, Dupuis, Speziale, Wieland... For example Speziale and Wieland http://arxiv.org/abs/1207.6348(The twistorial structure of loop-gravity transition amplitudes)

FreeImmirzi and Geometric Operator Spectra
Bianchi, Haggard http://arxiv.org/abs/1208.2228 (Bohr-Sommerfeld Quantization of Space)
We introduce semiclassical methods into the study of the volume spectrum in loop gravity. ... The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity.
Also http://arxiv.org/abs/1204.5122

Tetrad-handedness The Tetrad's sign could start to be included both in the classical theory upon which Loop gravity is based and in the quantum theory. Papers by Rovelli and others raise the issue: should the sign be included? If so, in which of two possible ways? How would this affect the quantum theory?
http://arxiv.org/abs/1205.0733
http://arxiv.org/abs/1207.5156

Histories refers primarily to Hartle's treatment of quantum mechanics which de-emphasizes observers and measurement--focusing on things we care about and want to predict or bet on happening. Histories are partitioned according to these concerns and a decoherence functional is defined on the partitions telling when sets are sufficiently independent to have ordinary probabilities.
http://arxiv.org/abs/gr-qc/0602013

Relativity and Thermodynamics/Statistical Mechanics of geometry is the theme of some recent papers by Rovelli, Jacobson, Smolin, Padmanabhan and others. Could the Einstein GR equation be (like PV = NkT) the equation of state describing overall behavior of microscopic variables (like the vast number of gas molecules whose collective behavior is summarized by PV = NkT.) If GR is the equation of state, what are the underlying degrees of freedom? Do spinfoams describe the underlying degrees of freedom for which EFE is the EoS?
http://arxiv.org/abs/1204.6349 http://arxiv.org/abs/1205.5529 http://arxiv.org/abs/1207.0505
Rovelli has a new paper in this connection. Just came out.
http://arxiv.org/abs/1209.0065
General relativistic statistical mechanics
(Submitted on 1 Sep 2012)
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = hbar dτ/ds, with k the Boltzmann constant, hbar the Planck constant, ds proper time and d tau the equilibrium thermal time.
Comments: A tentative second step in the thermal time direction, 10 years after the paper with Connes. The aim is the full thermodynamics of gravity. The language of the paper is a bit technical: look at the Appendix first

Dust is shorthand for the various approaches being used to recover a real physical Hamiltonian. Members of both the Erlangen and Warsaw groups have research along several related lines. This is familiar from cosmology and I think it's of considerable practical value.
http://arxiv.org/abs/1206.3807 http://arxiv.org/abs/1206.0658
 
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  • #105
In the preceding I listed 8 frontier categories, look back to see definitions and links to sample research. The third was too narrow and should be made to include Tensorial GFT. I have enlarged it here and tentatively call it Algebraic generalizations. Here is the revised stripped down list.

PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation.

Holonomy Spin Foam Models Spinfoam labels can be group elements. Finite groups are introduced. http://arxiv.org/abs/1208.3388 and references.

Algebraic generalizations: tensorGFT and twistorLQG See twistorLQG papers by Freidel, Livine, Dupuis, Speziale, Wieland... For example Speziale and Wieland http://arxiv.org/abs/1207.6348(The twistorial structure of loop-gravity transition amplitudes) For tensorial GFT see review by Razvan Gurau and references therein. http://arxiv.org/abs/1209.3252 (A review of the 1/N expansion in random tensor models)

FreeImmirzi and Geometric Operator Spectra Remarkable agreement of Loop with Bohr-Somerfeld quantization of geometry. immirzi provisionally let free to vary, which could have unforeseen consequences.

Tetrad-handedness The Tetrad's sign could start to be included both in the classical theory upon which Loop gravity is based and in the quantum theory.

Histories refers primarily to Hartle's treatment of quantum mechanics which de-emphasizes the classical observer and measuring device. Might be applicable to spinfoam dynamics.

Relativity and Thermodynamics/Statistical Mechanics of geometry is the theme of some recent papers by Rovelli, Jacobson, Smolin, Padmanabhan and others. Could the Einstein GR equation be (like PV = NkT) an equation of state?

Dust here is shorthand for the various approaches being used to recover time-evolution and a real physical Hamiltonian.

Progress occurring on some or all of these fronts could be expected to show up in the program at Loops 2013:
http://www.perimeterinstitute.ca/en/Events/Loops_13/Loops_13/
or possibly earlier at the GR20 meeting in Warsaw.
http://gr20-amaldi10.edu.pl
 
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  • #106
There's a direction I'd like to see, but that doesn't seem represented: what is the relationship between the two "visions" of classical general relativity emerging from LQG? The most definite sign is that the large j and small immirzi limit seems to give the Regge action. This is still dangerous because we know that depending on how the Regge action is "interpreted", results could be terrible (DT) or promising (CDT). The question is what interpretation does EPRL imply?

Dittrich is using tensor-network tools to try to coarse grain and get classical GR. Intuitively, that is more sensible. However, that does seem to ignore the clues from the large j limit - is she thinking that's a red herring, or is she secretly keeping that in mind?
 
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  • #107
atyy said:
... The most definite sign is that the large j and small immirzi limit seems to give the Regge action. This is still dangerous because we know that depending on how the Regge action is "interpreted", results could be terrible (DT) or promising (CDT). The question is what interpretation does EPRL imply?
...

As you know both DT and CDT deal with only a severely limited space of geometries which are constructed by sticking identical blocks together, either all the same shape and size or of two different types. This does not recover the full Regge theory. The Triangulation people HOPE that this limited space of geometries is somehow representative of the full range found in nature.

In assembling identical block they have found that problems can develop---on the one hand feathery structures form, not compact enough, and on the other hand structures that are too compact can form: a kind of dog-pile with too many blocklets adjacent to each other.

The full Regge calculus does not use identical blocklets. It uses what amounts to a lattice of variable length rods. The dynamics involves the lengths of the rods. I never heard of Regges type of GR having the pathologies of DT, and don't see how it even could have (though of course I might be wrong.)

Anyway, Atyy, I do not consider DT and CDT as being alternate "interpretations" of Regge. So of course I did not understand your post. I do not think that Loop faces a fork in the road between two "interpretations": a terrible (DT) and a promising (CDT).

However if you think it does face such a fateful fork in the road, perhaps you should write an email and tell one of the experts about it. Dittrich, Rovelli, Thiemann. Surely if there is some "danger" which they have overlooked they should be warned about it.
==============

My view is that the community is a substantial body of highly intelligent people who are alert to just about every potential problem connected to the approaches they are working on. I've watched the Loop approach evolve for almost 10 years now and they have repeatedly broken down roadblocks and surmounted obstacles, or found a way around them. There are certainly a lot of open problems---as Ashtekar recently said there are enough problems to keep the young researchers happily occupied for years to come. I think the community is always on the lookout for problems, and habitually goes after them vigorously. So it's exciting to watch. I don't expect Loop to stay vintage 2010 EPRL, I think it's already changing. But I do not know what the new shape will be and so am in suspense.
===============

Convergence is probably a central problem that several of the developments I listed are addressing. Certainly the "tetrad-handedness" work is aimed at that. But also "dust" because everything is much simpler when you have time and a real Hamiltonian. And I vaguely suspect that Dittrich group's "holonomy spin foam" enterprise is going to take a swipe at the convergence problem, or at least the classical limit via coarse-graining. I'm not clear about this, it's just my two-bit hunch. You may have some ideas about the holonomy spinfoam business.
 
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  • #108
Revised list of categories, with one omitted, look back to see definitions and links to sample research.
PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation.

Holonomy Spin Foam Models Spinfoam labels can be group elements. Finite groups. Kinship with lattice gauge theory. http://arxiv.org/abs/1208.3388 and references therein. New paper this week: http://arxiv.org/abs/1209.4539 .

Algebraic generalizations: tensorGFT and twistorLQG

FreeImmirzi and Geometric Operator Spectra

Tetrad-handedness

Relativity and Thermodynamics/Statistical Mechanics GR could be the equation of state and LQG the "molecules" (microscopic degrees of freedom).

Dust various means to recover time-evolution and real physical Hamiltonian.

Progress on any of these fronts could show up in the program at Loops 2013 and Warsaw GR20:
http://www.perimeterinstitute.ca/en/Events/Loops_13/Loops_13/
http://gr20-amaldi10.edu.pl
===================
Perhaps the most notable development in this connection this week was the appearance of a new Holonomy Spin Foam paper by Dittrich et al. Ill get the link.
http://arxiv.org/abs/1209.4539
Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
Bianca Dittrich, Frank Hellmann, Wojciech Kaminski
(Submitted on 20 Sep 2012)
In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied. We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space.
These considerations allow to derive the general form of the transfer operators which generates discrete time evolution. We will describe the transfer operators for some current models on the different boundary Hilbert spaces and highlight the role of the simplicity constraints determining the concrete form of the time evolution operators.
51 pages, 18 figures

The companion paper referred to here appeared last month:
http://arxiv.org/abs/1208.3388
Holonomy Spin Foam Models: Definition and Coarse Graining
Benjamin Bahr, Bianca Dittrich, Frank Hellmann, Wojciech Kaminski
(Submitted on 16 Aug 2012)
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin foam models to arbitrary, in particular finite groups. The similarity with standard lattice gauge theories allows to apply standard coarse graining methods, which for finite groups can now be easily considered numerically. We will summarize other holonomy and spin network formulations of spin foams and group field theories and explain how the different representations arise through variable transformations in the partition function. A companion paper will provide a description of boundary Hilbert spaces as well as a canonical dynamic encoded in transfer operators.
36 pages, 12 figures.
 
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  • #109
marcus said:
Anyway, Atyy, I do not consider DT and CDT as being alternate "interpretations" of Regge. So of course I did not understand your post. I do not think that Loop faces a fork in the road between two "interpretations": a terrible (DT) and a promising (CDT).

However if you think it does face such a fateful fork in the road, perhaps you should write an email and tell one of the experts about it. Dittrich, Rovelli, Thiemann. Surely if there is some "danger" which they have overlooked they should be warned about it.

They are well aware of it. http://arxiv.org/abs/1204.5394

(I corrected the link.)
 
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  • #110
==quote Atyy post #106==
There's a direction I'd like to see, but that doesn't seem represented: what is the relationship between the two "visions" of classical general relativity emerging from LQG? The most definite sign is that the large j and small immirzi limit seems to give the Regge action. This is still dangerous because we know that depending on how the Regge action is "interpreted", results could be terrible (DT) or promising (CDT). The question is what interpretation does EPRL imply?

Dittrich is using tensor-network tools to try to coarse grain and get classical GR. Intuitively, that is more sensible. However, that does seem to ignore the clues from the large j limit - is she thinking that's a red herring, or is she secretly keeping that in mind?
==endquote==

==quote me, post #107==
As you know both DT and CDT deal with only a severely limited space of geometries which are constructed by sticking identical blocks together, either all the same shape and size or of two different types. This does not recover the full Regge theory. The Triangulation people HOPE that this limited space of geometries is somehow representative of the full range found in nature.

In assembling identical block they have found that problems can develop---on the one hand feathery structures form, not compact enough, and on the other hand structures that are too compact can form: a kind of dog-pile with too many blocklets adjacent to each other.

The full Regge calculus does not use identical blocklets. It uses what amounts to a lattice of variable length rods. The dynamics involves the lengths of the rods. I never heard of Regges type of GR having the pathologies of DT, and don't see how it even could have (though of course I might be wrong.)

Anyway, Atyy, I do not consider DT and CDT as being alternate "interpretations" of Regge. So of course I did not understand your post. I do not think that Loop faces a fork in the road between two "interpretations": a terrible (DT) and a promising (CDT).

However if you think it does face such a fateful fork in the road, perhaps you should write an email and tell one of the experts about it. Dittrich, Rovelli, Thiemann. Surely if there is some "danger" which they have overlooked they should be warned about it.

My view is that the community is a substantial body of highly intelligent people who are alert to just about every potential problem connected to the approaches they are working on. I've watched the Loop approach evolve for almost 10 years now and they have repeatedly broken down roadblocks and surmounted obstacles, or found a way around them. There are certainly a lot of open problems---as Ashtekar recently said there are enough problems to keep the young researchers happily occupied for years to come. I think the community is always on the lookout for problems, and habitually goes after them vigorously. So it's exciting to watch. I don't expect Loop to stay vintage 2010 EPRL, I think it's already changing. But I do not know what the new shape will be and so am in suspense.
==endquote==

==quote Atyy, post#109 ===
They are well aware of it. http://arxiv.org/abs/1207.4596
==endquote==
http://arxiv.org/abs/1207.4596
The Construction of Spin Foam Vertex Amplitudes
Eugenio Bianchi, Frank Hellmann
(Submitted on 19 Jul 2012 (v1), last revised 21 Jul 2012 (this version, v2))
Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. They fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4 dimensional generalization of the Ponzano-Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett and Crane and Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentz-invariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine.
22 Pages. 1 Figure. I

==quote Atyy, post#109 ===
They are well aware of it. http://arxiv.org/abs/1204.5394

(I corrected the link.)
==endquote==
http://arxiv.org/abs/1204.5394
Discrete Gravity Models and Loop Quantum Gravity: a Short Review
Maite Dupuis, James P. Ryan, Simone Speziale
(Submitted on 24 Apr 2012 (v1), last revised 13 Aug 2012 (this version, v2))
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the Plebanski action. We discuss the role of discrete geometries in the spin foam formalism, with particular attention to the definition of the simplicity constraints.
31 pages.
 
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  • #111
I've listed 7 or so lines of development that bear watching but if I had to focus on one to see where it is going over the next 10 months, I believe I would pick Holonomy Spin Foam models. My hunch is it will produce the most by way of unexpected new stuff. I'm talking about the short term: results that will show up in the talks at Loops 2013 and Warsaw GR20:
http://www.perimeterinstitute.ca/en/Events/Loops_13/Loops_13/
http://gr20-amaldi10.edu.pl

A good brief introduction to HSF models is contained in the first part of this online seminar talk by Frank Hellmann:

http://relativity.phys.lsu.edu/ilqgs/hellmann090412.pdf
http://relativity.phys.lsu.edu/ilqgs/hellmann090412.wav
Holonomy Spin Foam Models: Asymptotic Dynamics

And here are the papers I was discussing a few posts back:
marcus said:
...
...
http://arxiv.org/abs/1209.4539
Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
Bianca Dittrich, Frank Hellmann, Wojciech Kaminski
(Submitted on 20 Sep 2012)
In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied. We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space.
These considerations allow to derive the general form of the transfer operators which generates discrete time evolution. We will describe the transfer operators for some current models on the different boundary Hilbert spaces and highlight the role of the simplicity constraints determining the concrete form of the time evolution operators.
51 pages, 18 figures

The companion paper referred to here appeared last month:
http://arxiv.org/abs/1208.3388
Holonomy Spin Foam Models: Definition and Coarse Graining
Benjamin Bahr, Bianca Dittrich, Frank Hellmann, Wojciech Kaminski
(Submitted on 16 Aug 2012)
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin foam models to arbitrary, in particular finite groups. The similarity with standard lattice gauge theories allows to apply standard coarse graining methods, which for finite groups can now be easily considered numerically. We will summarize other holonomy and spin network formulations of spin foams and group field theories and explain how the different representations arise through variable transformations in the partition function. A companion paper will provide a description of boundary Hilbert spaces as well as a canonical dynamic encoded in transfer operators.
36 pages, 12 figures.
Incidentally here is a YouTube in which one of the authors is singing the young theoretical physicist song:


A point to make is that Lattice Gauge Theory is a large well-developed and established body of mathematical methods, and they are extending LGT in a way that the lattice geometry can vary so as to include gravity.
And moreover it looks like their generalized or extended LGT is able to contain many of the spinfoam models which have been defined by Quantum Relativists, including EPRL, as special cases within a single group-labeled 2-complex format.
This is somehow the way that mathematical evolution ought to go. From having several comparatively ad hoc and partially successful theories, evolution moves towards a single less ad hoc more comprehensive theory that contains them---also evolution is towards more structural assumptions and fewer adjustable parameters (which incidentally makes a theory more firmly testable). This feels right as a direction to move in. And also it feels right to connect up with an already well-developed body of method like LGT. And that means having the 2-complexes be labeled by GROUP elements, rather than with spin or representation labels. I think. If they can make all this work then it seems (to my dim eyes) like the way to go.

For additional light on this, I think we should also check the 2011 (and perhaps earlier) posts by longtime PF member "f-h" in case there is anything relevant to the present situation. My impression is the posts are informative, coolly objective, and to the point regarding the QG research picture.
https://www.physicsforums.com/search.php?searchid=3391085
Francesca sometimes takes part in the same threads and gives a valuable second perspective.
 
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  • #112
A Dittrich Ryan paper just went on arxiv that will probably turn out to be quite important.
I wouldn't be surprised if Bianca Dittrich gives a seminar talk about it at Perimeter or discusses it when she has her ILQGS talk on 27 November. The title of that November seminar talk is still TBA.

This paper could have consequences, or so it seems to me. I'd like to hear others' comments. Here's the abstract:

http://arxiv.org/abs/1209.4892
On the role of the Barbero-Immirzi parameter in discrete quantum gravity
Bianca Dittrich, James P. Ryan
(Submitted on 21 Sep 2012)
The 1-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them Loop Quantum Gravity and Spin Foams. It facilitates the loop quantization programme and subsequently the Barbero-Immirzi parameter (gamma) arises in both the spectra of geometrical operators and in the dynamics provided by Spin Foams. However, the debate continues as to whether quantum physics should be Barbero-Immirzi parameter dependent. Starting from a discrete SO(4)-BF theory phase space, we find two possible reductions with respect to a discrete form of the simplicity constraints. The first reduces to a phase space with gamma-dependent symplectic structure and more generally in agreement with the phase space underlying Loop Quantum Gravity restricted to a single graph - a.k.a. Twisted Geometries. The second, fuller reduction leads to a gamma-independent symplectic structure on the phase space of piecewise-flat-linear geometries - a.k.a. Regge geometries. Thus, the gamma-dependence of physical predictions is related to the choice of phase space underlying the quantization.
16 + 12 pages
 
  • #113
Anyone following the research of Dittrich and her co-authors probably has already watched or might wish to watch this February 2012 Perimeter video lecture.
http://pirsa.org/12020142/
Coarse graining spin nets with tensor networks

The first slide gives motivation:
Spin foam models--candidates for quantum gravity--give (very) small scale physics.
Most important question: what do they describe at large scales?
Spin foams can be understood as lattice systems:
--Use coarse graining to construct effective models for larger scales.
--Problem: spin foam models for gravity have amazingly complicated amplitudes. No coarse graining methods available. Simplify models drastically, keep "spin foam construction principle", develop and test coarse graining methods.

A "spin net" is analogous to a spin foam but dimensionally reduced. Edges take the place of 2D plaquettes.
This is part of the drastic simplification used in this exploratory research. Subsequently, as we have seen, they work back up to "holonomy spin foam" models. Which are spin foams where the labels are elements g of a group G instead of spins and the like.

refers to http://arxiv.org/abs/1109.4927
http://arxiv.org/abs/1111.0967 (shorter version)
==quote page 3 of 1109.4927==
Spin foams are a particular class of lattice gauge models (see e.g. [63] for a recent review and [11] for a review emphasizing the relation to lattice gauge and statistical physics models). Such models are specified by variables, taking values in some group G, associated to the edges of a lattice (or more generally an oriented 2–complex) and weights associated to the plaquettes. They can thus also be termed plaquette models.
A related class of models, which will be introduced below, are so called edge or spin net models [11]. Here group variables are associated to the vertices of a lattice (or more generically an oriented graph or 1–complex) and weights to the edges. This class includes the well–known Ising models, based on the group Z2. Indeed it will turn out that the structures involved in a spin net model are very similar to those involved in spin foam models – just that where, for instance, weights are associated to 2D plaquettes for spin foams, weights are associated to 1D edges in spin nets, similarly for the group variables and so on. In this sense spin nets are a simpler or dimensionally reduced form of spin foams...
==endquote==
 
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  • #114
Narrowing down the areas we are watching will require taking some good and important work off the list, but I want to focus on just a few fronts where I think the development occurring could significantly change LQG in the near term. With some exceptions I will, for brevity, mention only one or two key papers in each category. Others could have been cited and were mentioned earlier in the thread.

PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation.
http://www-library.desy.de/cgi-bin/spifaacce/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29
Ashtekar, Agullo, Nelson http://arxiv.org/abs/1209.1609 (A Quantum Gravity Extension of the Inflationary Scenario)
Ashtekar, Agullo, Nelson http://arxiv.org/abs/1204.1288 (Perturbations in loop quantum cosmology)
Artymowski, Dapor, Pawlowski http://arxiv.org/abs/1207.4353 (Inflation from non-minimally coupled scalar field in loop quantum cosmology)
Many more papers identifying observable effects, by various author: Barrau, Grain, Cailleteau, Vidotto, Mielczarek, and others.

Group-labeled Spinfoams Spinfoam labels can be group elements. Finite groups are introduced. This could change the way LQG is formulated.
Bahr, Dittrich,Hellmann, Kaminski http://arxiv.org/abs/1208.3388 (Holonomy Spin Foam Models: Definition and Coarse Graining)
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary two-complexes as well as to generalize current spin foam models to arbitrary, in particular finite groups. The similarity with standard lattice gauge theories allows to apply standard coarse graining methods, which for finite groups can now be easily considered numerically. We will summarize other holonomy and spin network formulations of spin foams and group field theories and explain how the different representations arise through variable transformations in the partition function. A companion paper will provide a description of boundary Hilbert spaces as well as a canonical dynamic encoded in transfer operators.
Same authors http://arxiv.org/abs/1209.4539 (Holonomy Spin Foam Models: Boundary Hilbert spaces and canonical dynamics) .
Hellmann, Kaminski (Holonomy Spin Foam Models: Asymptotic dynamics of EPRL type models, in prep) .
For background, e.g. the transfer operator concept in spinfoam context:
Bahr, Dittrich, Ryan http://arxiv.org/abs/1103.6264 (Spin foam models with finite groups)

Immirzi Issues
Bianchi http://arxiv.org/abs/1204.5122 (Entropy of Non-Extremal Black Holes from Loop Gravity)
Dittrich, Ryan http://arxiv.org/abs/1209.4892 (On the role of the Barbero-Immirzi parameter in discrete quantum gravity)

Relativistic Thermodynamics/Statistical Mechanics of Geometry
Rovelli has a new paper out.
http://arxiv.org/abs/1209.0065
General relativistic statistical mechanics
(Submitted on 1 Sep 2012)
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = hbar dτ/ds, with k the Boltzmann constant, hbar the Planck constant, ds proper time and d tau the equilibrium thermal time.
9 pages. A tentative second step in the thermal time direction, 10 years after the paper with Connes. The aim is the full thermodynamics of gravity. The language of the paper is a bit technical: look at the Appendix first

Observer Space
Gielen, Wise http://arxiv.org/abs/1206.0658 (Linking Covariant and Canonical General Relativity via Local Observers)
See Derek Wise's ILQGS talk Tuesday 2 October:
http://relativity.phys.lsu.edu/ilqgs/
"Lifting General Relativity to Observer Space".
 
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  • #115
marcus said:
...
Observer Space
Gielen, Wise http://arxiv.org/abs/1206.0658 (Linking Covariant and Canonical General Relativity via Local Observers)
See Derek Wise's ILQGS talk Tuesday 2 October:
http://relativity.phys.lsu.edu/ilqgs/
"Lifting General Relativity to Observer Space".

The June 2012 paper was published in General Relativity and Gravitation.

Derek Wise has a new way to do canonical LQG and link it with Spinfoam QG. Anyone who wants to read up on this before Wise's talk on Tuesday can get additional intuition and more explanation of the notation from this slightly longer 2011 paper also by Gielen and Wise:

http://arxiv.org/abs/1111.7195
Spontaneously broken Lorentz symmetry for Hamiltonian gravity
Steffen Gielen, Derek K. Wise
In Ashtekar's Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields, presenting a significant obstacle to quantization, or additional (usually second class) constraints whose solution renders the resulting phase space variables harder to interpret in a spacetime picture. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation in which second class constraints never arise. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3,1) symmetry down to a subgroup SO(3)_y. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as 'Cartan geometrodynamics.' We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3,1) to SO(3) is not in conflict with Lorentz covariance.
10 pages. Published in Physical Review D.

I also found this 2009 solo paper by Wise helpful:
http://arxiv.org/abs/0904.1738
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
Derek K. Wise
Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant models in 3 dimensions include Einstein gravity in Chern-Simons form, as well as a new formulation of topologically massive gravity, with arbitrary cosmological constant, as a single constrained Chern-Simons action. In 4 dimensions the main model of interest is MacDowell-Mansouri gravity, generalized to include the Immirzi parameter in a natural way. I formulate these theories in Cartan geometric language, emphasizing also the role played by the symmetric space structure of the model. I also explain how, from the perspective of these Cartan-geometric formulations, both the topological mass in 3d and the Immirzi parameter in 4d are the result of non-simplicity of the Lorentz Lie algebra so(3,1) and its relatives. Finally, I suggest how the language of Cartan geometry provides a guiding principle for elegantly reformulating any 'gauge theory of geometry'.

Incidentally this was written for a special issue of the journal SIGMA which was dedicated to Élie Cartan.
 
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  • #116
I completely overlooked an important paper! It feeds into a potential near term reformulation of LQG. It is by Carrozza, Oriti, and Rivasseau about Tensorial GFT.
I should have had this paper on the 3rd quarter MIP poll (it came out in July) and somehow missed it.

Anyway, herewith another strand of current development, one of the halfdozen important lines of investigation that are part of the picture which I'm watching and trying to keep track of.

http://arxiv.org/abs/arXiv:1207.6734
http://inspirehep.net/record/1124138
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions.
Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau.
(Submitted on 28 Jul 2012)
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including: connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.
33 pages, 8 figures.

If anyone wants to register a vote for this COR paper on the MIP poll just let me know--I will tally up those votes along with the rest.

This paper has only been out a couple of days more than 2 months and it already has 5 cites.

Carrozza will be giving an ILQGS online seminar on it soon, so if anybody is interested in Tensor QFT they can listen and get the audio+slides version, with the other participants asking questions. The talk is scheduled for Tuesday 30 October.
 
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  • #117
November conference on Experimental Search for QG. The scheduled list of talks is out:
http://www.perimeterinstitute.ca/en/Events/Experimental_Search_for_QG/Experimental_Search_for_Quantum_Gravity%3A_the_hard_facts/
http://www.perimeterinstitute.ca/Events/Experimental_Search_for_QG/Schedule/

Revised update on some lines of investigation I think we should be keeping track of. For brevity only a few key papers are mentioned in each category. Others were mentioned earlier in the thread. Several of the themes here are covered in online seminar talks, e.g. ILQGS at http://relativity.phys.lsu.edu/ilqgs/

PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation.
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29 (the link gave 64 papers today, won't always work though)
Ashtekar, Agullo, Nelson http://arxiv.org/abs/1209.1609 (A Quantum Gravity Extension of the Inflationary Scenario)
Ashtekar, Agullo, Nelson http://arxiv.org/abs/1204.1288 (Perturbations in loop quantum cosmology)
Artymowski, Dapor, Pawlowski http://arxiv.org/abs/1207.4353 (Inflation from non-minimally coupled scalar field in loop quantum cosmology)
Many more papers identifying observable effects, by various author: Barrau, Grain, Cailleteau, Vidotto, Mielczarek, and others. Claus Kiefer's recent paper should be mentioned http://arxiv.org/abs/1210.0418 (Interpretation of the
Triad Orientations in Loop Quantum Cosmology) though being concerned with basic concepts rather than observable effects it does not fit in with these phenomenology papErs.

Group-labeled Spinfoams Spinfoam labels can be group elements. Finite groups are introduced. This could change the way LQG is formulated. Check out Hellmann's recent ILQGS talk 2 September.
Bahr, Dittrich,Hellmann, Kaminski http://arxiv.org/abs/1208.3388 (Holonomy Spin Foam Models: Definition and Coarse Graining)
Same authors http://arxiv.org/abs/1209.4539 (Holonomy Spin Foam Models: Boundary Hilbert spaces and canonical dynamics) .
Hellmann, Kaminski (Holonomy Spin Foam Models: Asymptotic dynamics of EPRL type models, in prep)
Bahr, Dittrich, Ryan http://arxiv.org/abs/1103.6264 (Spin foam models with finite groups)

Running G and gamma: black hole issues Bianchi's online ILQGS talk will be 16 October. I think his result helped set things up for yesterday's Ghosh and Perez paper.
Bianchi http://arxiv.org/abs/1204.5122 (Entropy of Non-Extremal Black Holes from Loop Gravity)
Dittrich, Ryan http://arxiv.org/abs/1209.4892 (On the role of the Barbero-Immirzi parameter in discrete quantum gravity)
Ghosh, Perez http://arxiv.org/abs/1210.2252 (The scaling of black hole entropy in loop quantum gravity)
They have G and the Immirzi γ run--going to G* and γ* in the UV limit. In the IR limit G=GNewton
We discuss some general properties of black hole entropy in loop quantum gravity from the perspective of local stationary observers at distance £ from the horizon. The present status of the theory indicates that black hole entropy differs from the low energy (IR) expected value A/(4G) (in natural units) in the deep Planckian regime (UV). The partition function is well defined if the number of non-geometric degrees of freedom gM(encoding the degeneracy of the area ap eigenvalue at a puncture p) satisfy the holographic bound gM < exp(ap/(4G)). Our framework provides a natural renormalization mechanism such that SUV ---> SIR=A/(4GNewton) as the scale £ flows.
​
For the scale they use a lowercase script L, which I can't type, so I use £ here.

Relativistic Thermodynamics/Statistical Mechanics of Geometry
Rovelli http://arxiv.org/abs/1209.0065 (General relativistic statistical mechanics)
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = hbar dτ/ds, with k the Boltzmann constant, hbar the Planck constant, ds proper time and d tau the equilibrium thermal time.​

Tensorial GFT Carroza will give an online talk on this at ILQGS on 30 October. Numerous others involved--I won't try to list.
Carrozza, Oriti, Rivasseau.http://arxiv.org/abs/arXiv:1207.6734 (Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions.)
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including: connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.​

Dittrich's ILQGS talk set for 27 November is still "TBA". It could be on Group-valued Spinfoam models or might be concerned with understanding the Immirzi parameter (Dittrich and Ryan have a recent paper on that.)
 
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  • #118
I'm trying to keep the list at no more than 5 topics. The last one should read (not simply "Tensorial GFT" but) Twistor LQG and Tensor GFT.

Twistor LQG and Tensor GFT Speziale will give an online ILQGS talk 13 November on a major Twistorial LQG paper he wrote with Wieland. I'll get the abstract in a moment. Carroza will talk about Tensorial GFT renormalization at ILQGS on 30 October. Several other researchers are involved on these two fronts--I won't try to list them.
Speziale, Wieland http://arxiv.org/abs/1207.6348 (The twistorial structure of loop-gravity transition amplitudes)
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial description, which brings new light on both classical and quantum aspects of the theory. At the classical level, we clarify the covariant properties of the discrete geometries involved, and the role of the simplicity constraints in leading to SU(2) Ashtekar-Barbero variables. We identify areas and Lorentzian dihedral angles in twistor space, and show that they form a canonical pair. The primary simplicity constraints are solved by simple twistors, parametrized by SU(2) spinors and the dihedral angles. We construct an SU(2) holonomy and prove it to correspond to the (lattice version of the) Ashtekar-Barbero connection. We argue that the role of secondary constraints is to provide a non trivial embedding of the cotangent bundle of SU(2) in the space of simple twistors. At the quantum level, a Schroedinger representation leads to a spinorial version of simple projected spin networks, where the argument of the wave functions is a spinor instead of a group element. We rewrite the Liouville measure on the cotangent bundle of SL(2,C) as an integral in twistor space. Using these tools, we show that the Engle-Pereira-Rovelli-Livine transition amplitudes can be derived from a path integral in twistor space. We construct a curvature tensor, show that it carries torsion off-shell, and that its Riemann part is of Petrov type D. Finally, we make contact between the semiclassical asymptotic behaviour of the model and our construction, clarifying the relation of the Regge geometries with the original phase space.​
Carrozza, Oriti, Rivasseau http://arxiv.org/abs/1207.6734 (Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions.)
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including: connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.​
 
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  • #119
Pardon my ignorance, but, how does this work under lorentzian transforms? I have no idea, but, would appreciate help.
 
  • #120
Chronos said:
...how does this work under lorentzian transforms?...

The basic references are 2010 papers by Rovelli Speziale and by Wieland:
http://arxiv.org/abs/1012.1739
Lorentz covariance of loop quantum gravity
Carlo Rovelli, Simone Speziale
(Submitted on 8 Dec 2010)
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. ...
... As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.
6 pages, 1 figure.

http://arxiv.org/abs/1012.1738
Complex Ashtekar variables and reality conditions for Holst's action
Wolfgang Wieland
(Submitted on 8 Dec 2010)
From the Holst action in terms of complex valued Ashtekar variables additional reality conditions mimicking the linear simplicity constraints of spin foam gravity are found... The resulting kinematical Hilbert space matches the original one of loop quantum gravity, that is for real valued Ashtekar connection. Our result perfectly fit with recent developments of Rovelli and Speziale concerning Lorentz covariance within spin-form gravity.
24 pages, 2 pictures
 
  • #121
I guess everybody who follows Loop gravity research knows the most recent definitive formulation was http://arxiv.org/abs/1102.3660 (the Zakopane lectures) and that was a fairly complete presentation of the theory as of 2010 which was what the papers that I just referenced, by Rovelli Speziale and by Wieland, were talking about.

what we are talking about in this thread is a prospective REFORMULATION which might or might not happen before the next Loops conference (July 2013). The Loops conference is held approximately every two years and the field is active enough so that the theory can change substantially---it can be interesting to watch.

One possible reformulation seems to be taking shape in the TWISTOR LQG paper by Speziale and Wieland. You will find the abstract to that if you look back 3 or 4 posts in this thread.
If there is a reformulation before July 2013, and a new standard version of the theory, and if it is the "twistorial" version proposed by Speziale and Wieland (for instance) then we can AGAIN ask about Lorentz covariance.

My guess is that the new version (if there is one) will be just as Lorentz covariant as the 2010 version. But of course that is in the future and we cannot know the future.

Right now I am keenly interested in identifying and focusing on the handful of new developments that could contribute to a nearterm reformulation of the theory. These are the things I expect to figure significantly in the Loops 2013 conference at Perimeter. Here is a checklist of short names--to help us (or at least me) keep them all in mind. All five bear watching:
  • PhenoCosmo
  • Group-tagged foam
  • Black holes where G and gamma run
  • Rel-istic Stat Mech and Thermo
  • Twistor Loop Tensor Group
These are abbreviated names so you and I can review the checklist in our minds without stumbling over a lot of of extra syllables. what they refer to is spelled out in more detail a few posts back in this thread, and links to sample research papers are given. For instance look back to post #117
 
  • #122
Gene Bianchi gives an important seminar talk tomorrow 16 October. It will be online.
http://relativity.phys.lsu.edu/ilqgs/
BTW He was recently awarded a Banting fellowship at Perimeter, which made the Perimeter website front page :-D
Tomorrow's talk is Horizon entropy from loop gravity

My personal hunch is that this frees the Immirzi to run with scale, as in the topic "Black holes where G and gamma run" on the mnemonic checklist given earlier. As I see it (others may differ) Bianchi's result leads into work by Ghosh Perez reported in their October paper, wherre both G and gamma run with scale.

What I'm aiming to do with that checklist is to keep 5 different topics or research fronts in mind---corresponding to investigation which I expect to play a role in the run-up to Loops 2013. Research themes that might figure in a near-term reformulation of the theory. I want the mnemonic topic names to be short and memorable so when I'm away from the computer, e.g. out taking a walk in the hills, or for some reason have a free moment, I can review the list and say over to myself the main features of what's going on in Loop research. Holonomy spinfoams just means you label the foam with GROUP elements instead of spins or group representation symbols. So it is no longer a spin-labeled foam, it is a group-labeled foam. So traveling thru the foam, different rotations and stuff happen to you corresponding to the group element living along the edge you are traversing. Bianca Dittrich's group is working on "holonomy spinfoam models" and to say that quickly as a short mnemonic I just call it group-tagged-foam.

Gene Bianchi's 16 October talk relates to the third topic on the list.

  • PhenoCosmo
  • Group-tagged foam
  • Black holes where G and gamma run
  • Relistic Stat Mech and Thermo
  • Twistor Loop Tensor Group

Stat Mech and Thermodynamics have NOT YET been give a fully General Relativistic treatment. So the fourth research thrust listed here is important. "Tensor Group" is short for "Tensorial Group Field Theory". 9 syllables instead of 3. And my personal guess is that the most promising nearterm reformulation of LQG is coming from "Twistorial Loop Quantum Gravity" (10 syllables instead of 3) as per work of Speziale Wieland.

To make it clearer to anyone new, I'll give a sample recent paper in each topic:
 
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  • #124
Sample of recent Perimeter talks ( http://pirsa.org ) relevant to the current QG directions, now online:

Understanding black hole entropy through the renormalization group
Speaker(s): Alejandro Satz
Abstract: It is known that the entanglement entropy of quantum fields on the black hole background contributes to the Bekenstein-Hawking entropy,and that its divergences can be absorbed into the renormalization of gravitational couplings. By introducing a Wilsonian cutoff scale and the concepts of ... read more
Date: 18/10/2012 - 2:30 pm
Series: Quantum Gravity
URL: http://pirsa.org/12100053/

Matter-wave clocks
Speaker(s): Holger Mueller
Abstract:
Date: 22/10/2012 - 9:15 am
Collection: Experimental Search for Quantum Gravity
URL: http://pirsa.org/12100124/

The cosmological constant and the emergence of the continuum
Speaker(s): Lorenzo Sindoni
Abstract: Naturalness problems that could be signaling the necessity a completion of an effective field theory with the introduction of an otherwise overlooked ingredient. The cosmological constant problem can be seen as a signal that the EFT for gravity, general relativity, is not correctly including t... read more
Date: 22/10/2012 - 12:00 pm
Collection: Experimental Search for Quantum Gravity
URL: http://pirsa.org/12100081/

Is there a MesoScale in Quantum Gravity? Is it a Non-Locality Scale?
Speaker(s): Stefano Liberati, Dionigi Benincasa, Laurent Freidel
Abstract:
Date: 22/10/2012 - 2:00 pm
Collection: Experimental Search for Quantum Gravity
URL: http://pirsa.org/12100082/

The highest-energy particles of the Universe as viewed by the Pierre Auger Observatory
Speaker(s): Markus Risse
Abstract: One century after the seminal balloon flights of Victor Hess, the Pierre Auger Observatory aims at unveiling some of the mysteries of the highest-energy cosmic rays: what are their sources? Is there an end to the spectrum? What kind of particles are they? Are there signatures of new physics or... read more
Date: 23/10/2012 - 9:00 am
Collection: Experimental Search for Quantum Gravity
URL: http://pirsa.org/12100089/

Is spacetime fundamentally discrete?
Speaker(s): Bianca Dittrich, Daniele Oriti, Tobias Fritz, Seth Major, Roberto Percacci
Abstract: Modelling continuum dynamics on discrete space time
We will discuss perfect discretizations which aim at mirroring exactly continuum physics on a given lattice. Such discretizations avoid typical artifacts like Lorentz violation, energy dissipation, p... read more
Date: 24/10/2012 - 9:00 am
Collection: Experimental Search for Quantum Gravity
URL: http://pirsa.org/12100100/

Dynamical Dimensional Reduction
Speaker(s): Martin Reuter, Astrid Eichhorn, Dejan Stojkovic
Abstract: Dynamical dimensional reduction and Asymptotic Safety
The effective average action approach to Quantum Einstein Gravity (QEG) is discussed as a natural framework for exploring the scale dependent Riemannian geometry and multifractal micro-structure of ... read more
Date: 24/10/2012 - 11:30 am
Collection: Experimental Search for Quantum Gravity
URL: http://pirsa.org/12100104/
 
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  • #125
Bee Hossenfelder has a summary of the recent conference (Experimental Search for Quantum Gravity) at her blog.
http://backreaction.blogspot.com/2012/10/esqg-2012-conference-summary.html

Sylvain Carrozza gave his seminar talk at ILQGS today and the slides and audio are available online:
Renormalization of Tensorial Group Field Theories
http://relativity.phys.lsu.edu/ilqgs/carrozza103012.pdf
http://relativity.phys.lsu.edu/ilqgs/carrozza103012.wav

Simone Speziale is up next, in one week (6 November)
Twistorial structure of loop quantum gravity transition amplitudes
 
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  • #126
As context to the Carrozza seminar talk today, here is an October 1 post of mine.
marcus said:
I completely overlooked an important paper! It feeds into a potential near term reformulation of LQG. It is by Carrozza, Oriti, and Rivasseau about Tensorial GFT.
I should have had this paper on the 3rd quarter MIP poll (it came out in July) and somehow missed it.

Anyway, herewith another strand of current development, one of the halfdozen important lines of investigation that are part of the picture which I'm watching and trying to keep track of.

http://arxiv.org/abs/arXiv:1207.6734
http://inspirehep.net/record/1124138
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions.
Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau.
(Submitted on 28 Jul 2012)
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including: connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.
33 pages, 8 figures.

If anyone wants to register a vote for this COR paper on the MIP poll just let me know--I will tally up those votes along with the rest.

This paper has only been out a couple of days more than 2 months and it already has 5 cites.

Carrozza will be giving an ILQGS online seminar on it soon, so if anybody is interested in Tensor QFT they can listen and get the audio+slides version, with the other participants asking questions. The talk is scheduled for Tuesday 30 October.

Here, again, are the links to Carrozza's seminar talk.

Renormalization of Tensorial Group Field Theories
http://relativity.phys.lsu.edu/ilqgs/carrozza103012.pdf
http://relativity.phys.lsu.edu/ilqgs/carrozza103012.wav
The talk is good and there is extensive questioning and discussion by Joseph Ben Geloun, Lee Smolin, Laurent Freidel, Carlo Rovelli, Abhay Ashtekar, Daniele Oriti and I believe others whose names I didn't catch.
 
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  • #127
If it turns out (as judging from the interest in Carrozza Oriti Rivasseau's paper it conceivably might) that TGFT (tensorial group field theory) serves as basis for a nearterm reformulation of LQG/SF, then those who wish to follow what is going on in the field could find this tutorial by Krajewski useful:
http://arxiv.org/abs/1210.6257
Group field theories
Thomas Krajewski
(Submitted on 23 Oct 2012)
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field theories, merging ideas from tensor models and loop quantum gravity. This lecture is organized as follows. In the first section, we present basic aspects of quantum field theory and matrix models. The second section is devoted to general aspects of tensor models and group field theory and in the last section we examine properties of the group field formulation of BF theory and the EPRL model. We conclude with a few possible research topics, like the construction of a continuum limit based on the double scaling limit or the relation to loop quantum gravity through Schwinger-Dyson equations
58 pages, Lectures given at the "3rd Quantum Gravity and Quantum Geometry School", March 2011, Zakopane
 
  • #128
For several reasons I think this paper represents a critical development in the emerging reformulation that I'm trying to understand
http://arxiv.org/abs/1210.0418
Interpretation of the triad orientations in loop quantum cosmology
Claus Kiefer, Christian Schell
(Submitted on 1 Oct 2012)
Loop quantum cosmology allows for arbitrary superpositions of the triad variable. We show here how these superpositions can become indistinguishable from a classical mixture by the interaction with fermions. We calculate the reduced density matrix for a locally rotationally symmetric Bianchi I model and show that the purity factor for the triads decreases by decoherence. In this way, the Universe assumes a definite orientation.
12 pages, 1 figure

This is the first paper in which I remember the density matrix and its purity index trace(ρ2) playing a central role in LQC. This is a more general notion of quantum state--the vonNeumann algebra, or C*-algebra approach to QM.

We can see signs of this shift (in how things are formulated) appearing in LQG, in other papers. But this is the first time I'm aware of it's happening in the Cosmology application LQC.
 
  • #129
As a reminder, here are a half-dozen research areas where this approach to Quantum Gravity is being reshaped. All the ILQGS talks mentioned are now online with the sole exception of Bianca Dittrich's scheduled for 27 November.

twistorLQG (Speziale's ILQGS talk and 1207.6348)
tensorialGFT (Carrozza's ILQGS talk and 1207.6734)
holonomySF (Hellmann's ILQGS talk and 1208.3388)
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

I think the last topic is critical, namely general relativistic thermodynamics (broadly interpreted to include statistical mechanics and the operator algebra formulation).

First it is clear that to be fully successful LQG has to encompass the LQC bounce, with matter and inhomogeneity--we already see that beginning to happen. In encompassing the bounce the model seemingly must include the dissipation or shrinkage of horizons and their vonNeumann entropy, with the emergence of a pure state.

I recently added the Kiefer and Schell paper http://arxiv.org/abs/1210.0418 as an indication of where that is going. Kiefer Schell have the purity/mixedness of quantum states run on a continuum from zero to one. A state is a trace-class operator ρ on the hilbert space, a generalized "density matrix". Pure states are those for which tr(ρ2) = 1, a kind of "purity index". As these gradually decohere, the purity index comes down from 1 to zero. In Kiefer Schell's case the quantum state of geometry does this as it interacts with the matter in the environment. If I'm not mistaken, LQG dynamics will be extended to include states of this density matrix ρ type (as Kiefer and Schell do with LQC) and Rovelli's September paper is a step in this direction. Then the problem will be to understand how the purity index of the state is driven *up* during bounce. Intuitively there is a "release of information" when Planckian density density is approached, and information that had become inaccessible becomes accessible (in the repellent gravity phase of the bounce.) I could of course have this wrong, so I'm looking for other viewpoints.
 
  • #130
Let's just look at the last 4 of the above LQG initiatives. HSF answers criticism by Alexandrov, so we can disregard the latter.
holonomySF (Hellmann's ILQGS talk and 1208.3388)
See Hellmann's comment here:
https://www.physicsforums.com/showthread.php?p=4162474#post4162474
(If anyone is new to the discussion, Frank Hellmann posts here as f-h.)
Dittrich may have some more to say about holonomy spin foam models in her ILQGS talk on 27 November.
============
The main thing I have to say right now is that in a certain sense all of the last three are working towards the same goal. The point is that a thermal state automatically breaks Lorentz invariance e.g. page 18 of Connes Rovelli gr-qc/9406019. So it is a no-brainer that any thermal state would have its own inherent notion of time. The challenge is to realize this in GR, what is a thermal state in GR which is timeless?
If one can do that, one finesses "dust". Thermal time and dust are reading from the same page of the book.
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

And hybrid LQC (the breakground work of Agullo Ashtekar Nelson) is a way of putting an infinity of DoF into LQG cosmology, around the time of the bounce before conventional inflation begins. This gives a way to grasp the thermal state. So these three things are, I think, aimed at one goal.
 
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  • #131
In two days Dittrich will give an online ILQGS talk, the last one of the fall semester.

Nov. 27 Coarse graining: towards a cylindrically consistent dynamics Bianca Dittrich Perimeter Institute
http://relativity.phys.lsu.edu/ilqgs/ (online audio and slides PDF)

This will probably be an important talk to hear for anyone wishing to follow developments in LQG (or quantum gravity in general). This will presumably be the second Holonomy Spin Foam (HSF) talk at ILQGS this fall and based on
http://arxiv.org/abs/1208.3388
Holonomy Spin Foam Models: Definition and Coarse Graining

An earlier HSF talk was given Sept. 4 Holonomy Spin Foam Models: Asymptotic Dynamics by Frank Hellmann of Albert Einstein Institute

Other HSF papers which have appeared recently:
http://arxiv.org/abs/1209.4539
Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators
Bianca Dittrich, Frank Hellmann, Wojciech Kaminski

http://arxiv.org/abs/1210.5276
Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations
Frank Hellmann, Wojciech Kaminski

Holonomy spinfoam models are a different kind of spinfoam, similar to lattice connection theories in that they use group element labels living on the 2-complex. Notice that the title of an HSF talk or paper does not necessarily signal that it is HSF by including the word "holonomy". The title of the Hellmann Kaminski paper simply says "spin foam lattice gauge gravity" and you are supposed to understand that it is HSF (a point clearly made in the introduction). I gather from comments made that people working on HSF (coarse graining, asymptotics, dynamics...) have indicated they see the approach as overcoming some obstacles/unresolved questions in the earlier version of spinfoam.

Dittrich is one the main people in charge of organizing next year's Loops conference at PI, and also the senior organizer of the LQG parallel sessions at the GR-20 conference to be held next year in Warsaw.
GR-20 Warsaw (week of 7 July):
http://gr20-amaldi10.edu.pl/index.php?id=18
Loops 2013 Perimeter Institute (week of 21 July):
http://www.perimeterinstitute.ca/conferences/loops-13
__________________

If I had to bet now concerning the future course of LQG development---near future, see where we are in July 2013---I think I would say, as of now, that the two most interesting lines of development are HSF and a nexus of ideas I would call
"GR thermo, C*-algebra, hybrid LQC"
I see these things as coming together and clarifying, among other things, the LQC bounce (which is where the opening to phenomenology seems to be IMHO). Hybrid LQC puts Fock into the bounce picture--lots of particles and geometric fluctuations. (See latest Agullo Ashtekar Nelson.)
The C*-algebra formalism gives a way to do general covariant statistical quantum mechanics. (See new version of http://arxiv.org/abs/1209.0065 that was uploaded 19 November with a new section (Appendix B4) at the end with title something like "GC statistical QM".
 
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  • #132
The slides PDF for Dittrich's talk is already online.
http://relativity.phys.lsu.edu/ilqgs/dittrich112712.pdf
It's about Coarse Graining spinfoam QG and spin net etc. and it is an exceptionally
clear set of slides. Refers to a lot of work in progress (w.i.p.) and recent papers.
Try here http://relativity.phys.lsu.edu/ilqgs/ later in the day to see if audio is online.

You can already learn quite a bit about their approach to coarse graining (and thus the largescale limit) simply by examining the slides. Sample page of computer code. Many diagrams.

EDIT: The audio also is now on line! It's a good talk. Here's the audio.
http://relativity.phys.lsu.edu/ilqgs/dittrich112712.wav
Most of the question time is Dittrich discussing with Ashtekar and Rovelli. Around minute 2, more exactly 2:20, from the end Francesca gets in a question.
Bianca's group is running computer simulations of their coarse-graining strategies. The slide graphics of how the coarsegraining works is well thought out and communicates effectively (when there is the audio explanation along with it).

The type of spinfoam they use is HSF (holonomy sf) and the 2D analog of that is what they call spin net. Both have group element labels rather than some other kind (e.g. spins, twistors). But much of the work involves highly simplified toy models. Not QG. Regular lattices. This does not mean it's trivial or uninteresting! On the contrary, I would say. It looks to me as if an effective method of coarsegraining for 4D spinfoam QG is being developed, and one that can be implemented numerically. If that is the case it will be a substantial advance.
 
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  • #133
I need to elaborate the nexus of ideas mentioned in posts #130 and 131 that seem to be coming to a better understanding of the LQC bounce.
"GR thermo, GC statistical QM, hybrid LQC, pre-inflationary dynamics, matter bounce"
marcus said:
Holonomy spinfoam models are a different kind of spinfoam, similar to lattice connection theories in that they use group element labels living on the 2-complex...
...I gather from comments made that people working on HSF (coarse graining, asymptotics, dynamics...) have indicated they see the approach as overcoming some obstacles/unresolved questions in the earlier version of spinfoam.
...
If I had to bet now concerning the future course of LQG development---near future, see where we are in July 2013---I think I would say, as of now, that the two most interesting lines of development are HSF and a nexus of ideas I would call
"GR thermo, C*-algebra, hybrid LQC"
I see these things as coming together and clarifying, among other things, the LQC bounce (which is where the opening to phenomenology seems to be IMHO). Hybrid LQC puts Fock into the bounce picture--lots of particles and geometric fluctuations. (See latest Agullo Ashtekar Nelson.)
The C*-algebra formalism gives a way to do general covariant statistical quantum mechanics. (See new version of http://arxiv.org/abs/1209.0065 that was uploaded 19 November with a new section (Appendix B4) at the end with title something like "GC statistical QM".

Back in post #130 I mentioned the paper Pre-inflationary LQC the PennState people (Agullo Ashtekar Nelson*) have in preparation. Now there's another paper contributing to our understanding of the LQC bounce, this time by Wilson-Ewing (PennState PhD now at Marseille):

The Matter Bounce Scenario in Loop Quantum Cosmology
Edward Wilson-Ewing
(Submitted on 27 Nov 2012)
In the matter bounce scenario, a dust-dominated contracting space-time generates scale-invariant perturbations that, assuming a nonsingular bouncing cosmology, propagate to the expanding branch and set appropriate initial conditions for the radiation-dominated era. Since this scenario depends on the presence of a bounce, it seems appropriate to consider it in the context of loop quantum cosmology where a bouncing universe naturally arises. It turns out that quantum gravity effects play an important role beyond simply providing the bounce. Indeed, quantum gravity corrections to the Mukhanov-Sasaki equations significantly modify some of the results obtained in a purely classical setting: while the predicted spectra of scalar and tensor perturbations are both almost scale-invariant with identical small red tilts in agreement with previous results, the tensor to scalar ratio is now expected to be r≈ 9 x 10-4, which is much smaller than the original classical prediction. Finally, for the predicted amplitude of the scalar perturbations to agree with observations, the critical density in loop quantum cosmology must be of the order ρcrit ~ 10-9 ρPlanck.
8 pages

Francesca's November 2012 review talk at the Stockholm fundamental cosmology conference already discusses the QG corrected Mukhanov-Sasaki equation as per Wilson-Ewing. This Loop matter-bounce paper could have a profound impact. Corrected M-S has the same ρ/ρPl term as the QG corrected Friedmann eqn. Both corrections are "Planck-suppressed", IOW they only take effect as the energy density approaches Planck density. Including the matter-bounce means that the rebound of a collapsing classical phase occurs sooner at much lower density.

*Nelson was at PennState and is now at Nijmegen, he also gave a talk at the Stockholm cosmology conference.
 
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  • #134
Classical/semiclassical corroboration--chaos, volume gap

New work by Hal Haggard--solo and with Eugenio Bianchi--and by Berndt Müller (10,000 lifetime cites, previous work in nuclear theory and hep-phenomenology) reveals classical physics evidence supporting LQG quantized view of space and the volume gap. This is the idea that the LQG volume operator should have a gap between zero and the first positive eigenvalue.

Intuitively that there should be a lowest volume that you can measure. Space geometry discreteness idea.

What does chaos, a property exhibited by classical dynamics in certain cases, have to do with this?

It seems as if the recent work by Haggard, Bianchi, Müller, Coleman-Smith... could be opening up a new line of LQG research--something we need to notice and try to understand if we're following the field. I'll fetch some links.

http://arxiv.org/abs/1211.7311
Pentahedral volume, chaos, and quantum gravity
Hal M. Haggard
(Submitted on 30 Nov 2012)
We show that chaotic classical dynamics associated to the volume of discrete grains of space leads to quantal spectra that are gapped between zero and nonzero volume. This strengthens the connection between spectral discreteness in the quantum geometry of gravity and tame ultraviolet behavior. We complete a detailed analysis of the geometry of a pentahedron, providing new insights into the volume operator and evidence of classical chaos in the dynamics it generates. These results reveal an unexplored realm of application for chaos in quantum gravity.
5 pages, 4 figures

http://lanl.arxiv.org/abs/1212.1930
A "Helium Atom" of Space: Dynamical Instability of the Isochoric Pentahedron
C. E. Coleman-Smith, B. Muller
(Submitted on 9 Dec 2012)
We present an analysis of the dynamics of the equifacial pentahedron on the Kapovich-Millson phase space under a volume preserving Hamiltonian. The classical dynamics of polyhedra under such a Hamiltonian may arise from the classical limit of the node volume operators in loop quantum gravity. The pentahedron is the simplest nontrivial polyhedron for which the dynamics may be chaotic. We consider the distribution of polyhedral configurations throughout the space and find indications that the borders between certain configurations act as separatrices. We examine the local stability of trajectories within this phase space and find that locally unstable regions dominate although extended stable regions are present. Canonical and microcanonical estimates of the Kolmogorov-Sinai entropy suggest that the pentahedron is a strongly chaotic system. The presence of chaos is further suggested by calculations of intermediate time Lyapunov exponents which saturate to non zero values.
20 Pages, 19 Figures

http://arxiv.org/abs/1102.5439
Discreteness of the volume of space from Bohr-Sommerfeld quantization
Eugenio Bianchi, Hal M. Haggard
(Submitted on 26 Feb 2011 (v1), last revised 6 Jun 2011 (this version, v2))
A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.
4 pages, 4 figures; to appear in PRL

http://arxiv.org/abs/1208.2228
Bohr-Sommerfeld Quantization of Space
Eugenio Bianchi, Hal M. Haggard
(Submitted on 10 Aug 2012)
We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity. Moreover, it provides new geometrical insights into the degeneracy of this spectrum and the maximum and minimum eigenvalues of the volume on intertwiner space.
32 pages, 10 figures

It was surprising how close the semiclassical numbers were to the numbers computed using the full LQG quantum theory. At that point they were using TETRAHEDRON volume dynamics. Notice the gradual ratcheting up of complexity---now to pentahedron---in the newer papers.

In case anyone is interested in Berndt Müller's earlier research interests http://inspirehep.net/author/B.Muller.1/
 
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  • #135
Yesterday's Pirsa talk on chaos and quantum mechanics:
http://pirsa.org/12120036/ (online video)
Quantum Chaos, Information Gain and Quantum Tomography.
Speaker(s): Vaibhav Madhok
Abstract: Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In recent years, attempts have been made to address this question from the perspective of quantum information theory. It is in this spirit that we study the connection between quantum chaos and information gain in the time series of a measurement record used for quantum tomography...
... We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two.
Date: 11/12/2012 - 3:30 pm

What I highlighted is the general question that the papers by Hal Haggard and by Berndt Müller also seem to be getting at. Particularly http://arxiv.org/abs/1211.7311
and http://arxiv.org/abs/1212.1930

I continue to be impressed by how many active directions of research in LQG there are at present. I listed some of them a few posts back. I suspect the map of LQG is going to be quite different in July when Loops 2013 is held, from what it was at the previous Loops conference held in 2011 at Madrid.
http://www.perimeterinstitute.ca/conferences/loops-13
 
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  • #136
Is it possible that Mielczarek is on to something? Can we give meaning to what he says here which seems so incomprehensible the first time I read it?
At Planck scale, or thereabouts, the spacetime causal structure would be numbed as if by a massive shot of novocaine, into non-existence. All lines of communication go dead?

But he is working in a LQG cosmology context here. Wouldn't there be a bounce well before that density is reached?

http://arxiv.org/abs/1212.3527
Asymptotic silence in loop quantum cosmology
Jakub Mielczarek
(Submitted on 14 Dec 2012)
The state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In particular, such behavior was anticipated by Belinsky, Khalatnikov and Lifgarbagez (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counterpart at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density ρ = ρc/2, where ρc is the maximal allowed energy density, being of the order of the Planck energy density. At energy densities ρ > ρc/2, the universe becomes 4D Euclidean space without causal structure. Therefore, the asymptotic silence appears to be an intermediate state of space between the Lorentzian and Euclidean phases.
4 pages, 3 figures

I would like to dismiss this as too far-out, but don't feel that I can. LQG research is going in a bewildering variety of different directions right now. I don't remember it ever being so multi pronged in past years.
 
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  • #137
I'll recall post #129 at the top of this page, just so we don't get so intrigued by detail that we lose track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference (Loops 13 July of next year).
marcus said:
As a reminder, here are a half-dozen research areas where this approach to Quantum Gravity is being reshaped.

==quote post #129==
...
twistorLQG (Speziale's ILQGS talk and 1207.6348)
tensorialGFT (Carrozza's ILQGS talk and 1207.6734)
holonomySF (Hellmann's ILQGS talk and 1208.3388)
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522 and 1212.5183)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

I think the last topic is critical, namely general relativistic thermodynamics (broadly interpreted to include statistical mechanics and the operator algebra formulation).

First it is clear that to be fully successful LQG has to encompass the LQC bounce, with matter and inhomogeneity--we already see that beginning to happen. In encompassing the bounce the model seemingly must include the dissipation or shrinkage of horizons and their vonNeumann entropy, with the emergence of a pure state.

I recently added the Kiefer and Schell paper http://arxiv.org/abs/1210.0418 as an indication of where that is going. Kiefer Schell have the purity/mixedness of quantum states run on a continuum from zero to one. A state is a trace-class operator ρ on the hilbert space, a generalized "density matrix". Pure states are those for which tr(ρ2) = 1, a kind of "purity index". As these gradually decohere, the purity index comes down from 1 to zero. In Kiefer Schell's case the quantum state of geometry does this as it interacts with the matter in the environment. If I'm not mistaken, LQG dynamics will be extended to include states of this density matrix ρ type (as Kiefer and Schell do with LQC) and Rovelli's September paper is a step in this direction. ...
==endquote==

Claus Kiefer's recent LQG paper is a step in the direction of the "star algebra" formulation of QG---where the basic mathematical object is (M,ω) an observables algebra M with a state function ρ: M→ℂ which gives the correlations and expectation values.

In the the entanglement entropy part of above post, I added a reference (in red) to a new paper by Bianchi and Myers:
http://arxiv.org/abs/1212.5183
On the Architecture of Spacetime Geometry
Eugenio Bianchi, Robert C. Myers
(Submitted on 20 Dec 2012)
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein-Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity and loop quantum gravity, as well as the AdS/CFT correspondence.
8 pages, 1 figure
 
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  • #138
The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

The Bianchi Myers paper noted in previous post seems remarkably rich in useful ideas--I'm not sure what the right word is, "fertile" maybe? At least to me, it suggests how, if LQG were put in C*-algebra form, one might define 3D REGIONS by subsets of the algebra satisfying an entanglement-area condition. Note the word "architecture" in the title, as indicative of how the authors are thinking.

In any case it adds an exciting motivation to the (M, ω) world format. How can a smooth manifold picture emerge from some instance of (M, ω)? Perhaps one can state a condition in terms of entanglement entropy of certain subsets of the algebra. This is mentioned simply for motivation and I won't speculate further. I will list the various reformulation fronts in a different order.

Loop cosmology is getting into inhomogeneous regimes with multiple degrees of freedom and exploring "pre-inflationary" dynamics in more detail. Provisionally I'm calling that "hybrid loop cosmology" because several recent papers join existing LQC bounce with Fock space in a kind of hybrid. I can't list all the papers developing inhomogeneous LQC, so will just mention a couple.
hybrid LQC
Agullo Ashtekar Nelson—An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (http://arxiv.org/abs/1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)

It's hard to know what to call the next development. Perhaps "C*-quantum gravity, T-time, and entanglement entropy".
Work towards general covariant (GC) analysis such as GC-thermo, GC statistical (quantum) mechanics seems to motivate an (M,ω) formulation. This finally solves the time problem because one gets an observer-independent (Tomita) flow on the observables algebra. But how do we recover the regional STRUCTURE of space in the (M,ω) context? I see Bianchi Myers paper in this light. The key word "architecture" in the title is a signal. Also Kiefer Schell paper leans in that direction.
C*-quantum gravity, T-time, entanglement
Rovelli—General relativistic statistical mechanics (http://arxiv.org/abs/1209.0065)
Bianchi—Horizon entanglement entropy and universality of the graviton coupling (ILQGS talk and http://arxiv.org/abs/1211.0522)
Bianchi Myers—On the Architecture of Spacetime Geometry (http://arxiv.org/abs/1212.5183)
Kiefer Schell—Interpretation of the triad orientations in loop quantum cosmology (http://arxiv.org/abs/1210.0418)
Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)
 
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  • #139
The ILQGS (international LQG seminar) is a good pointer to active areas of QG research---one can see this in the previous post: several of the themes we identified were represented not only by recent papers but also by Fall 2012 semester talks. Jorge Pullin organizes the ILQGS and I think he does a great job.

Part of the Spring 2013 schedule is posted now and we can examine it to help get a clearer picture of current research developments.

Jan 29th Entanglement in loop quantum gravity — Eugenio Bianchi — Perimeter Institute.
Feb 12th Dynamical chaos and the volume gap — Hal Haggard — CPT Marseille
Feb 26th Gravity electroweak unification — Stephon Alexander — Haverford College
Mar 12th .....
Mar 26th Bianchi I LQC — Brajesh Gupt — LSU

The 26 March talk by Gupt exemplifies the current trend in Loop cosmology towards cosmic models which are less uniform: not homogeneous and isotropic. For many years at the beginning LQC deal with uniform models with a correspondingly small number of degrees of freedom. Now they are running models which achieve a bounce (where the singularity used to be) but involve more complex variation. The socalled "Bianchi I" models are only one example.

Others of the talks are on topics that feature in our 4th quarter MIP poll. I have to go---there's more to say about this.
 
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  • #140
As suggested in preceding post, we can get an idea of the active directions in Loop research by seeing what the Spring semester ILQGS talks will be about. For instance, I think the 29 January talk by Bianchi will be important and could be based on his November 2012 paper. This I think is a breakthrough paper, as I will explain.
http://arxiv.org/abs/1211.0522
Horizon entanglement entropy and universality of the graviton coupling
Eugenio Bianchi
(Submitted on 2 Nov 2012)
We compute the low-energy variation of the horizon entanglement entropy for matter fields and gravitons in Minkowski space. While the entropy is divergent, the variation under a perturbation of the vacuum state is finite and proportional to the energy flux through the Rindler horizon. Due to the universal coupling of gravitons to the energy-momentum tensor, the variation of the entanglement entropy is universal and equal to the change in area of the event horizon divided by 4 times Newton's constant - independently from the number and type of matter fields. The physical mechanism presented provides an explanation of the microscopic origin of the Bekenstein-Hawking entropy in terms of entanglement entropy.
7 pages

This is a breakthrough because a radical simplification. You can calculate the entanglement entropy, in this case, just from the entanglement entropy of the gravitons alone.
You do not have to put matter fields into the calculation because the gravitons FEEL the matter thoroughly and reflect its entanglements.

Eventually, I suspect, the entropy associated with different regions will be algebraically definable in a C* context, based on correlations between observables. The entropy-area relation will facilitate exploring the geometry in a situation where no manifold is given to start with. This will advance the program of recovering geometric relationships in a C* picture of the world, IMHO. So I think this is an outstanding paper with long-range significance. If someone disagrees with this assessment of 1211.0522, please tell me--I'd be interested in hearing a different opinion.

So later this month, as 29 January approaches, some of us will probably decide to take a look at the November paper to prepare for listening to the online seminar titled:
Entanglement in loop quantum gravity by Eugenio Bianchi.
 
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  • #141
The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

Now with only 6 months left before conference there has appeared what I think is maybe the MOST ambitious reformulation initiative. This is via GAUGE NETWORK and GAUGE FOAM analogs by Marcolli and van Suijlekom (at Caltech and Nijmegen). These are analogous to the spin networks and spin foams that are already used in the current LQG formulation, except now the chunks of space are equipped with noncommutative geometry.

http://arxiv.org/abs/1301.3480
Gauge networks in noncommutative geometry
Matilde Marcolli, Walter D. van Suijlekom
(Submitted on 15 Jan 2013)
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences...
...
The people:
http://www.its.caltech.edu/~matilde/
http://www.math.ru.nl/~waltervs/index.php?page=home
(Walter Daniel van Suijlekom b. 1978, dual career as professional musician, interesting. PhD 2005 at SISSA Trieste. Since 2007 postdoc at Nijmegen, same place as Renate Loll. Has taught some interesting courses at Nijmegen including NCG, i.e. spectral geometry.)

I think this Marcolli van Suijlekom initiative could lead to a C* algebra formulation of LQG. Already they have a Hamiltonian and time evolution of gauge networks (at least in some case they are considering). At the end of the paper there is a proposal for how to do gauge FOAMS and what the PARTITION FUNCTION should look like, i.e. a PATH INTEGRAL approach coming out. And it looks in a very general way rather like what you see in Zakopane Lectures (2011)

The idea is to have chunks of ALMOST COMMUTATIVE space (represented by finite dimensional spectral triples, spectral polyhedra?) at the vertices of the network, and have the links be morphisms somehow joining the vertices. Almost commutative spectral geometry is how Connes and friends realized the Standard Model. So in spirit very much like current LQG except chunks of almost commutative space at the vertices instead of chunks of ordinary commutative space.

I think these things are all related and am not sure what to call this development. Perhaps "C*-quantum gravity, T-time, entanglement entropy, gauge networks".
I should recall that work towards general covariant (GC) analysis such as GC-thermo, GC statistical (quantum) mechanics seems to motivate a star algebra (M,ω) formulation because this finally solves the time problem. One gets an observer-independent (Tomita) flow on the observables algebra. Then how do we recover the regional STRUCTURE of space in the (M,ω) context? I see Bianchi Myers paper in this light. The key word "architecture" in the title is a signal. Also Kiefer Schell paper leans in that direction.
======================
C*-quantum gravity, T-time, entanglement, gauge networks
Marcolli van Suijlekom—Gauge networks in noncommutative geometry (http://arxiv.org/abs/1301.3480)
Rovelli—General relativistic statistical mechanics (http://arxiv.org/abs/1209.0065)
Bianchi—Horizon entanglement entropy and universality of the graviton coupling (ILQGS talk and http://arxiv.org/abs/1211.0522)
Bianchi Myers—On the Architecture of Spacetime Geometry (http://arxiv.org/abs/1212.5183)
Kiefer Schell—Interpretation of the triad orientations in loop quantum cosmology (http://arxiv.org/abs/1210.0418)

===================
The LQG-LQC bridge, hybrid LQC, matter bounce
Alesci and Cianfrani have established a clear derivation of LQC from the full LQG theory--canonically quantizing first and then reducing to the cosmo case. Loop cosmology is getting into inhomogeneous regimes with multiple degrees of freedom and exploring "pre-inflationary" dynamics in more detail. Provisionally I'm calling that "hybrid loop cosmology" because several recent papers join existing LQC bounce with Fock space in a kind of hybrid. I can't list all the papers developing inhomogeneous LQC, so will just mention a small sample.
Alesci Cianfrani—Quantum-Reduced Loop Gravity: Cosmology (http://arxiv.org/abs/1301.2245)
Agullo Ashtekar Nelson—An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (http://arxiv.org/abs/1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
Wilson-Ewing—The Matter Bounce Scenario in Loop Quantum Cosmology (http://arxiv.org/abs/1211.6269)
====================

Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)
 
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  • #142
The twistorial reformulation of LQG has taken a big step forward with:
http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

To get a sense of Wieland you could watch some of this Perimeter talk (February 2012):
http://pirsa.org/12020129/
 
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  • #143
In 3 days, Bianchi's ILQGS talk: Entanglement entropy in LQG
The slides PDF may be posted beforehand (this has happened with ILQGS) and the URL will probably be: http://relativity.phys.lsu.edu/ilqgs/bianchi012913.pdf
After the talk the audio URL will probably be http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav
He has shown that the BH horizon entropy and the CEH (cosmic event horizon) entropy can both be understood as entanglement.
The state on the accessible side must be MIXED because entangled with the state on the other side. This gives a simple handle on the entropy, as he shows.

The talk will necessarily take as its point of departure his November paper. http://arxiv.org/abs/1211.0522 This is a classic: a major landmark, very short (4 pages), simply worded, and effecting a radical change of perspective.
The November paper was not set in anyone theory---e.g. not specifically a LQG paper. It was quite general.
So now we will see what's new since then, what specifically QG development can have grown out of it.

If one is rereading the papers in order to prepare to understand the online talk, there is also Bianchi's December paper with Rob Myers (http://arxiv.org/abs/1212.5183) which I mentioned two posts back.
 
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  • #144
marcus said:
The twistorial reformulation of LQG has taken a big step forward with:

I think it should be remarked that this time time is only a dimension like in GR.
 
  • #145
  • #146
The audio for Bianchi's 29 Jan ILQGS talk has been posted:
http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav

Next up (12 February) is Hal Haggard's talk:
Dynamical chaos and the volume gap

http://relativity.phys.lsu.edu/ilqgs/
Interestingly, Haggard's research has already been "covered" (as they say in the music business) by a prominent particle theorist named Berndt Müller.
The existence of a smallest observable volume (a gap in the vol operator spectrum between zero and the smallest positive eigenvalue) is the key to the discreteness/finiteness feature of LQG. There is an analogy between "energy conserving" Hamiltonian dynamics and "volume preserving" shape-shifting of polyhedra that let's one treat it as a dynamical system. Classical chaos tends to go along with discrete spectrum at the quantum level. So the work here is supportive.
==============

Here are some of the more interesting papers that appeared this month, giving us an idea of directions the field will be going in 2013. I'll have to factor these into the reformulation themes already identified in this thread.

It is important that the relation between LQG and the cosmology application LQC has been clarified by the Alesci Cianfrani and the Engle papers. One can do the symmetry reduction AFTER quantization. So there is no obstacle to viewing LQC as a straightforward application of the full theory. In fact Engle shows that one can EMBED LQC in full theory without ever invoking the piecewise linear category, or fixing on some particular graph structure.
This opens the way to testing full LQG theory by confronting LQC predictions with early universe observation. So it's a 2013 milestone.

http://arxiv.org/abs/1301.1264
Inflation as a prediction of loop quantum cosmology
Linda Linsefors, Aurelien Barrau
(Submitted on 7 Jan 2013)

http://arxiv.org/abs/1301.2245
Quantum-Reduced Loop Gravity: Cosmology
Emanuele Alesci, Francesco Cianfrani
(Submitted on 10 Jan 2013)
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.

http://arxiv.org/abs/1301.6210
Embedding loop quantum cosmology without piecewise linearity
Jonathan Engle
(Submitted on 26 Jan 2013)
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory,...The present paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well-defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed, and at no point is the piecewise linear category used. ...

==========
The Marcolli Suijlekom paper opens a possible path to building the standard matter field model into LQG. It let's the NODES of the network be SPECTRAL GEOMETRY CHUNKS instead of ordinary geometry chunks. Alain Connes and others have shown that a version of the standard matter model lives in spectral geometry. It does not have to be laid on by hand. A LQG spin network is re-named a "gauge network" when the nodes are spectral.

http://arxiv.org/abs/1301.3480
Gauge networks in noncommutative geometry
Matilde Marcolli, Walter D. van Suijlekom
(Submitted on 15 Jan 2013)
We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. ... beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences...

=============
Wolfgang Wieland's paper puts the whole business of secondary constraints, reality conditions etc on a new footing. We should recognize that it changes the terms of the discussion. So it is a major paper.

http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures
 
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  • #147
The papers of Engle and by Alesci Cianfrani mentioned in above post indicate that Loop cosmology can be embedded in the full LQG theory, or derived from it. Reductions to the interesting cases for cosmology can be done AFTER the quantum theory is constructed. It has been pointed out that this opens the way for testing the full LQG theory. It has to give the right answers about the early universe.

Hence the relevance of this paper by Agullo Ashtekar Nelson that appeared today:
http://arxiv.org/abs/1302.0254
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 1 Feb 2013)
Using techniques from loop quantum gravity, the standard theory of cosmological perturbations was recently generalized to encompass the Planck era. We now apply this framework to explore pre-inflationary dynamics. The framework enables us to isolate and resolve the true trans-Planckian difficulties, with interesting lessons both for theory and observations. Specifically, for a large class of initial conditions at the bounce, we are led to a self consistent extension of the inflationary paradigm over the 11 orders of magnitude in density and curvature, from the big bounce to the onset of slow roll. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects ---such as a modification of the consistency relation between the ratio of the tensor to scalar power spectrum and the tensor spectral index, as well as a new source for non-Gaussianities--- which could extend the reach of cosmological observations to the deep Planck regime of the early universe.
64 pages, 15 figures

The main actively researched QG rival to LQG in modeling the early universe has been the Asymptotic Safe QG program. String and Causal Dynamical Triangulations don't seem to have much to say about the start of expansion---or at least not much is being written from those perspectives.
However, the AS program may have experienced a severe setback with the appearance of Hamber's result that a QG theory in which the cosmological constant runs cannot be general covariant. For some discussion:
https://www.physicsforums.com/showthread.php?t=668612
 
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  • #148
Marcus, what about some kind of "status report" of LQG?

We have several new ideas in the field:
- non-interacting dust defining field of physical observers and physical Hamiltonian
- spinor / twistor variables and changes in the constraint structure
- some relations (but still no proof of equivalence) for canonical and spin foam models

What do you think? Where are the main results and what are the key issues?
 
  • #149
tom.stoer said:
Marcus, what about some kind of "status report" of LQG?

We have several new ideas in the field:
- non-interacting dust defining field of physical observers and physical Hamiltonian
- spinor / twistor variables and changes in the constraint structure
- some relations (but still no proof of equivalence) for canonical and spin foam models

What do you think? Where are the main results and what are the key issues?

That's a nice question. I will have to respond in several stages. First, a general introduction, the overall context, how LQG fits into the picture, where I think it's going.

The overall program is Quantum Cosmology (QC). Humans should understand particle theory in dynamic geometry because our historic big job now is to accurately model the start of expansion. We have an enormous amount of data resulting from the start of expansion---a "big bounce" I expect but that remains to be seen.

That is the top of the mountain that the LQG climbers and other teams are working towards. So locating their current "status" means (for me) locating relative to that goal. Where are they relative to that goal?

Part of the goal, also, is to understand where Dark Matter comes from, and if possible to explain the size of the classical Cosmological Constant (part of understanding dynamic geometry.)

The path up the mountain is zig-zag. So I am always watching out for these surprise changes, that we have seen the Quantum Relativists make several times over the years.

Besides the particle theory of the "big bounce" (or whatever was the Beginning-of-Expansion) there is also the thermodynamics and statistical mechanics of the "big bounce" (or whatever was the Beginning-of-Expansion). Maybe that has tended to be overlooked, but it is a persistent interesting problem. I will set it aside for the moment and just think about the quantum particle relativist side.

This is why I think it is so important to review Marciano's May 2012 talk, and to hear Alexander's talk tomorrow (26 February 2013).
 
  • #150
As I see it, LQG is a subfield of LQC. Much (perhaps most) Loop community work is now Cosmo-related. Papers by Engle and by Alesci show a good bridge, symmetry reduction can be done at the quantum level. And symmetry restrictions are gradually being relaxed--eg the work on Bianchi-One cosmologies.

If you think of this as "the tail wagging the dog" then as an aggregate research effort the tail is now bigger than the dog.

We tend to think of the main Loop research centers as Marseille, Perimeter, PennState, Erlangen, Warsaw...

But Agullo and Nelson are very important in cosmology and Agullo is at Cambridge and Nelson is at Nijmegen. And now suddenly I have realized that Dartmouth is an important place on the Loop map. That is where Marciano is--currently postdoc working with Alexander.

The Dartmouth people seem to start with particle theory and cosmology, and with unification at a classical level, and then move naturally into a spin foam quantization!

That makes me think that what Loop is depends on what you start with. It is a bunch of background-free lattice gauge theory techniques that have so far been explored using classic GR as a starting point. But the Dartmouth people show me that you do not have to be limited to starting with GR---you can start with more.

That is what tomorrow's talk by Alexander is about, and what the 7 May talk by Marciano will be about.

So this probably is a major revolution in Loop---another turning point in the zig-zag climb up the mountain.

Also it is a very necessary revolution, because to understand the Big Bounce one has to understand matter fields behavior in extreme dynamic geometry conditions. So one probably needs some BF-like extension of Plebanski action, and a background-free lattice quantization. Spinfoam in other words. This understanding is the mountain top that people are working towards, and we can think of Spinfoam work so far as practice for that ascent.

Anyway that is my two cents. It is how I see the general overall context: where LQG fits in.
I will try to assemble some kind of "progress report" for you on a more detailed level, although I'm no expert in the business.

EDIT: BTW Marciano's May 2012 talk is http://pirsa.org/12050079/
also BTW it would help me, if you have any comments on the above, to know your reactions.
It may be a while before I get to the job of assembling details of the picture and responses to this much, from you, could I think be very helpful.

EDIT: Reminder, the link to get slides PDF and audio for tomorrow's talk by Alexander is
http://relativity.phys.lsu.edu/ilqgs/
The title of the talk is Gravity Electroweak Unification
 
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