Reformulation of Loop gravity in progress, comment?

[marcus]

I forgot TWISTORS when listing active lines of Loop research which could feature in whatever reformulation takes shape at the July 2013 Perimeter conference. This just came out:
http://arxiv.org/abs/1207.6348
The twistorial structure of loop-gravity transition amplitudes
Simone Speziale, Wolfgang M. Wieland
(Submitted on 26 Jul 2012)
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 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.
39 pages

So a revised list:
PhenoCosmo (bounce early universe cosmology is where pheno enters most directly)
TwistorLQG
FreeImmirzi
Tetrad-handedness
Stacking
Histories
Thermo
Dust

For reference purposes, helping to look up papers by author, I'll tag these lines of research with (very incomplete) lists of names:
PhenoCosmo (Barrau, Grain, Pawlowski, Cailleteau, Agullo, Nelson, Vidotto,...)
TwistorLQG (Levine, Dupuis, Speziale, Wieland,...)
FreeImmirzi (Bianchi, ...)
Tetrad-handedness (Rov., ...)
Stacking (Lew., ... )
Histories (Hartle, Schroeren?, Craig?)
Thermo (Jac., Smo., Pad., ...)
Dust (Lew., Thiem., Wise, ...)[/QUOTE]

 

[marcus]

Twistors are having a significant impact on Loop. We need to learn a bit about them.
Here is a nice tutorial with 15 transparencies sketched by Penrose. He is able to think and communicate in a highly graphic way, a bit like a cartoonist. The text is only 4 pages, if you print it out, but you might want to print out a few or all of the transparencies as well: just click on an individual slide and you can print it.
http://users.ox.ac.uk/~tweb/00006/index.shtml

The tutorial (based on a talk by Penrose) was prepared and put on line by Fedja Hadrovich, who also has this more mathy less visual introduction called Twistor Primer, that might be helpful as a supplement:
http://users.ox.ac.uk/~tweb/00004/index.shtml

My impression is that the entry of twistors into Loop geometry/gravity was by way of
work by Freidel, Livine, Dupuis, Tambornino, Speziale and Wieland.

One thing that served to whet my interest in this version ("twistorial LQG") was a Perimeter video talk by Wieland. Wieland is at Marseille but in February this year he was visiting at PI (doing some work with Bianchi I think) and gave a cogent and (to me unexpectedly understandable) seminar on a spinor/twistor way of treating Ashtekar variables and doing canonical Loop gravity. (!) I will get the PIRSA link to that video talk.

http://pirsa.org/12020129/
Spinor Quantisation for Complex Ashtekar Variables
Speaker(s): Wolfgang Wieland
Abstract: During the last couple of years Dupuis, Freidel, Livine, Speziale and Tambornino developed a twistorial formulation for loop quantum gravity.
Constructed from Ashtekar--Barbero variables, the formalism is restricted to SU(2) gauge transformations.
In this talk, I perform the generalisation to the full Lorentzian case, that is the group SL(2,C).
The phase space of SL(2,C) (i.e. complex or selfdual) Ashtekar variables on a spinnetwork graph is decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a clean derivation of the solution space of the reality conditions of loop quantum gravity.
Key features of the EPRL spinfoam model are perfectly recovered.
If there is still time, I'll sketch my current project concerning a twistorial path integral for spinfoam gravity as well.
Date: 29/02/2012 - 4:00 pm

In the sense used here, two spinors make a twistor. A twistor can be called a "bi-spinnor".
Basically just saying ℂ² x ℂ² = ℂ⁴
And Wieland is using pairs of spinnors on the links of his spinnetworks.

 

[marcus]

So the updated list of active Loop areas I want to watch are:

PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation. Recent papers by Ashtekar, Agullo, Nelson and by Artymowski, Dapor, Pawlowski.

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

FreeImmirzi was a consequence of Bianchi and others' black hole entropy result S=A/4. It appears to have exciting and unpredictable implications for the theory.
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

Stacking refers to Lewandowski group's 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

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

Thermodynamics of geometry is the theme of some recent papers by 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

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

========================

 

[marcus]

Connes is back in the game!
That means that Grimstrup's effort to implement the Spectral Standard Model of particle theory in the Loop QG is likely to get some attention at next July's Loops conference.
http://pirsa.org/index.php?p=speaker&name=Jesper_Grimstrup
http://pirsa.org/09100143/
On Semi-classical States of Quantum Gravity and Noncommutative Geometry
Speaker(s): Jesper Grimstrup
Abstract: The idea behind an intersection between loop quantum gravity and noncommutative geometry is to combine elements of unification with a setup of canonical quantum gravity. In my talk I will first review the construction of a semi-finite spectral triple build over an algebra of holonomy loops. Here, the loop algebra is a noncommutative algebra of functions over a configurations space of connections, and the interaction between the Dirac type operator and the loop algebra captures information of the kinematical part of canonical quantum gravity. Next, I will show how certain normalizable, semi-classical states are build which connects the spectral triple construction to the Dirac Hamiltonian in 3+1 dimensions. Thus, these states can be interpreted as one-particle fermion states in an ambient gravitational field. This analysis indicates that the spectral triple construction involves matter degrees of freedom.
Date: 14/10/2009 - 4:00 pm

Here is Connes' recent paper. MTd2 spotted it and added it to our bibliography.
http://arxiv.org/abs/1208.1030
Resilience of the Spectral Standard Model
Ali H. Chamseddine, Alain Connes
(Submitted on 5 Aug 2012)
We show that the inconsistency between the spectral Standard Model and the experimental value of the Higgs mass is resolved by the presence of a real scalar field strongly coupled to the Higgs field. This scalar field was already present in the spectral model and we wrongly neglected it in our previous computations. It was shown recently by several authors, independently of the spectral approach, that such a strongly coupled scalar field stabilizes the Standard Model up to unification scale in spite of the low value of the Higgs mass. In this letter we show that the noncommutative neutral singlet modifies substantially the RG analysis, invalidates our previous prediction of Higgs mass in the range 160--180 Gev, and restores the consistency of the noncommutative geometric model with the low Higgs mass.
13 pages

This August paper consists largely of a re-examination of their April 2010 paper (which is reference [2] and is cited over and over again). The 2010 paper treats the Spectral Standard Model and a sketch of the unification of forces roughly along "Big Desert" lines. As I understand it, in the analysis for the earlier paper a "Higgs singlet" appeared, as well as a Higgs doublet. The assumption was made that this scalar field would not affect the Higgs mass. Unless I'm mistaken it is this part of the 2010 picture which they are now revising. I should include the abstract.

http://arxiv.org/abs/1004.0464/
Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
Ali H. Chamseddine, Alain Connes
(Submitted on 3 Apr 2010)
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this notation is used to determine the spectral data of the standard model. The particle spectrum with all of its symmetries is derived, almost uniquely, under the assumption of irreducibility and of dimension 6 modulo 8 for the finite space. The reduction from the natural symmetry group SU(2)xSU(2)xSU(4) to U(1)xSU(2)xSU(3) is a consequence of the hypothesis that the two layers of space-time are finite distance apart but is non-dynamical. The square of the Dirac operator, and all geometrical invariants that appear in the calculation of the heat kernel expansion are evaluated. We re-derive the leading order terms in the spectral action. The geometrical action yields unification of all fundamental interactions including gravity at very high energies. We make the following predictions:
(i) The number of fermions per family is 16.
(ii) The symmetry group is U(1)xSU(2)xSU(3).
(iii) There are quarks and leptons in the correct representations.
(iv) There is a doublet Higgs that breaks the electroweak symmetry to U(1).
(v) Top quark mass of 170-175 Gev.
(v) There is a right-handed neutrino with a see-saw mechanism.
Moreover, the zeroth order spectral action obtained with a cut-off function is consistent with experimental data up to few percent. We discuss a number of open issues. We prepare the ground for computing higher order corrections since the predicted mass of the Higgs field is quite sensitive to the higher order corrections. We speculate on the nature of the noncommutative space at Planckian energies and the possible role of the fundamental group for the problem of generations.
56 pages

I spent some time searching through the April 2010 paper and could not find the relevant passage. There was mention of something possibly relevant on page 26, right before equation (6.17), and also section 9.4 on page 33. But I couldn't be certain.Steven Weinberg gave some useful perspective in this 2009 wide-audience talk, link to which I should keep handy:

 

[marcus]

Back in post #93, when listing significant areas of Loop gravity development to watch I gave links to sample research in all but the first on the list: what for want of a handier term I am calling "PhenoCosmo" for phenomenological quantum cosmology. I think of this as perhaps the most critical research front, because cosmology is the main arena in which QG (quantum relativity, quantum geometry and matter) theories will necessarily be tested.

In the Loop case the Pheno studies involve calculating the observable effects of the Bounce and subsequent Bounce-triggered inflation. This search, while not perfect and containing a few of what may be considered "false positives", currently finds 62 papers of which most are of the desired sort. The papers all appeared in 2009 or later, and are ranked by number of times cited.

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

Here's a revised listing with some PhenoCosmo sample links:
PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation.
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: Phenomenology and Fundamental LQC Parameters)
http://arxiv.org/abs/1003.4660 (Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves)

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 was a consequence of Bianchi and others' black hole entropy result S=A/4. It appears to have exciting and unpredictable implications for the theory.
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

Stacking refers to Lewandowski group's 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

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

Thermodynamics of geometry is the theme of some recent papers by 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

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

 

[marcus]

One of the categories in the preceding post needs enlargement.

FreeImmirzi and Operator Spectra
http://arxiv.org/abs/1204.5122 This, and several others along the same lines establish the Loop black hole entropy relation S = A/4 independent of the the Immirzi parameter γ. At the same time, there is another approach to studying the range of possible values of this parameter, since the geometric operator spectra depend on γ. It turns out that it is possible to define semiclassical (Bohr-Sommerfeld) volume OUTSIDE the LQG context and thus have semiclassical eigenvalues to compare with those of LQG. I have the sense that this work is just getting started. Here is a recent paper along those lines.

Note however the footnote on page 4:
"Here l_P is the Planck length and γ is the Barbero-Immirzi parameter. They should both be understood as coupling constants of the theory. Throughout the remainder of the paper we will take l_P = γ = [STRIKE]h[/STRIKE] = 1."

As yet I do not see it constraining the variation of γ, but this line of investigation could lead to that. So far what it does is tend to confirm that the LQG geometric operators are correct, have the right spectra, because of the agreement with an alternative quantization of space.

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

 

[marcus]

The main idea of this thread is a hunch that a reformulation of Loop is in progress and I'm trying to identify the areas to watch, in order to spot the main direction. In earlier posts I identified 7 areas and () may have missed the most, or one of the most significant ones: holonomy spin foams, where e.g. edges can be labeled with group elements instead of representations.
Here are a couple of papers that were recently cited "in preparation".

[28] B. Bahr, B. Dittrich, F. Hellmann, and W. Kaminski, “Holonomy Spin Foam Models:
Boundary Hilbert spaces and canonical dynamics,” (2012) .

[29] F. Hellmann and W. Kaminski, “Holonomy Spin Foam Models: Asymptotic dynamics of EPRL type models,” (2012) .

These have not come out yet but should appear this year. I'll try to explain why I think this line of investigation is important. Here is the paper which cites them.

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

As an interested non-expert observer I now think this is probably the most significant Loop QG paper that has appeared so far this quarter (or perhaps a longer period of time).

The transfer operator concept, in spinfoam context, is introduced here:
and also here:
http://arxiv.org/abs/1103.6264
Spin foam models with finite groups
Benjamin Bahr, Bianca Dittrich, James P. Ryan
(Submitted on 31 Mar 2011)
Spin foam models, loop quantum gravity and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community we provide an introduction to some essential concepts in the loop quantum gravity, spin foam and group field theory approach and point out the many connections to lattice field theory and condensed matter systems.
47 pages, 6 figures

See equations (6.1) (6.8) (6.15) (6.20) starting on page 19
Further reference on page 37.
For possibility of slicing spinfoams see Dittrich Höhn 0912.1817
There is a type of transfer operator which is based on "tent moves".
For tent move concept see http://arxiv.org/abs/0912.1817 Fig.1 on page 6 and Fig.2 on page 7.

 

[marcus]

We should also have these links handy, to help understand the connection of this paper with the topic I earlier called "Stacking". Maybe I should have called it "Stacking, group labels, coarse graining, and the transfer operator." :-) All these ideas seem to be interrelated, where they involve spinfoam QG. The presence of finite groups is interesting.
http://arxiv.org/abs/1112.3567
Operator Spin Foams: holonomy formulation and coarse graining
Benjamin Bahr
(Submitted on 15 Dec 2011)
A dual holonomy version of operator spin foam models is presented, which is particularly adapted to the notion of coarse graining. We discuss how this leads to a natural way of comparing models on different discretization scales, and a notion of renormalization group flow on the partially ordered set of 2-complexes.
5 pages, 3 figures, to appear in Journal of Physics: Conference Series. (JPCS)

http://arxiv.org/abs/1010.4787
Operator Spin Foam Models
Benjamin Bahr, Frank Hellmann, Wojciech Kamiński, Marcin Kisielowski, Jerzy Lewandowski
(Submitted on 22 Oct 2010)
The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with demanding consistency with splitting the edges, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on Spin(4) BF spin foam model is exactly the way we tend to view 4d quantum gravity, starting with the BC model and continuing with the EPRL or FK models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. We discuss the examples: BF spin foam model, the BC model, and the model obtained by application of our framework to the EPRL intertwiners.
19 pages, 11 figures. Published in Classical and Quantum Gravity (2011)

There was also a third, related, paper:
http://arxiv.org/abs/1107.5185
Feynman diagrammatic approach to spin foams
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
36 pages, 23 figures. Published in Classical and Quantum Gravity (2012)

The idea of TRANSFER OPERATOR, highlighted in red in preceding post, is also introduced in Dittrich's 2011 Escorial talk:
http://www.ucm.es/info/giccucm/Escorial2011/Dittrich.pdf
See the slide immediately before the Summary, at the end. And also a couple of slides before that.
The index for the July 2011 Escorial QInfo+StatM school is here:
http://www.ucm.es/info/giccucm/Escorial2011/
There seem to have been several interesting talks given at that school.

 

[marcus]

http://arxiv.org/abs/1208.3388
Holonomy Spin Foam Models: Definition and Coarse Graining
Benjamin Bahr, Bianca Dittrich, Frank Hellmann, Wojciech Kaminski

the "Groups 29" conference has been running all this past week. These four people are all invited speakers. What do you imagine their talks have been about?

http://www.cim.nankai.edu.cn/activites/conferences/hy20120820/index.htm
There is an important biennial series of conferences held once every two years, called the
International Colloquium on Group-Theoretical Methods in Physics
Most recently one was held this past week at Tianjin China This is the 29th in the series so it's called "Groups 29". It concludes tomorrow, 26 August.

The invited Loop speakers are almost all young researchers---postdocs plus some first-time faculty. It's a remarkable list.
Session 8: Loop Quantum Gravity
Chair: Jerzy Lewandowski (University of Warsaw, Poland)

Invited Speakers (Titles and Abstracts)

Emanuele Alesci (University of Erlangen-Nurnberg, Germany)
Benjamin Bahr (University of Cambridge, UK)
Norbert Bodendorfer (University of Erlangen-Nuremberg, Germany)
You Ding (Beijing Jiaotong University, China)
Bianca Dittrich (Perimeter Institute for Theoretical Physics, Canada)
Jonathan Engle (Florida Atlantic University, USA)
Marc Geiller (APC-University Paris 7, France)
Hal Haggard (Centre de Physique Theorique de Luminy, France)
Frank Hellmann (Albert Einstein Institute, Germany)
Wojciech Kaminski (Albert Einstein Institute, Germany)
Marcin Kisielowski (University of Warsaw, Poland)
Yongge Ma (Beijing Normal University, China)
Wolfgang Wieland (Universite de la Mediterranee (Marseille), France)
Mingyi Zhang (Aix-Marseille Universite, France)

Though I have some guesses about the conference presentation topics, I can't say for sure because the "Titles and Abstracts" link does not work with either of my browsers.
Maybe someone else can get the talk titles and post them here.

A list of the Tianjin talks might have clues as to what direction the changing formulation of Loop QG is going.

 

[atyy]

http://www.ucm.es/info/giccucm/Escorial2011/Dittrich.pdf

No more spin networks - just spin nets

I think it's interesting that spin nets are dual to spin foams. I had wrongly thought they'd be like spin networks.

Her final point: "can apply tensor network renormalization schemes: stay tuned" !

 

[marcus]

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.

 

[atyy]

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 .

 

[marcus]

For an up-to-date summary of current definitions, main results, and important open problems see Rovelli's July 2012 Stockholm slides:
http://www.cpt.univ-mrs.fr/~rovelli/RovelliStockholmSpinFoam.pdf

A specialized talk about LQG black hole thermodynamics, clarifying how to think about the recent results and identifying open questions:
http://www.cpt.univ-mrs.fr/~rovelli/RovelliStockholmTermo.pdf

 

[marcus]

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

 

[marcus]

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

 

[atyy]

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?

 

[marcus]

... 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.

 

[marcus]

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.

 

[atyy]

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.)

 

[marcus]

==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.

 

[marcus]

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:

...
...
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.

 

[marcus]

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

 

[marcus]

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==

 

[marcus]

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".

 

[marcus]

...
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.

 

[marcus]

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.

 

[marcus]

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=G_Newton

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 g_M(encoding the degeneracy of the area a_p eigenvalue at a puncture p) satisfy the holographic bound g_M < exp(a_p/(4G)). Our framework provides a natural renormalization mechanism such that S_UV ---> S_IR=A/(4G_Newton) 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.)

 

[marcus]

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.​

 

[Chronos]

Pardon my ignorance, but, how does this work under lorentzian transforms? I have no idea, but, would appreciate help.

 

[marcus]

...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