Reformulation of Loop gravity in progress, comment?

[marcus]

I guess everybody who follows Loop gravity research knows the most recent definitive formulation was http://arxiv.org/abs/1102.3660 (the Zakopane lectures) and that was a fairly complete presentation of the theory as of 2010 which was what the papers that I just referenced, by Rovelli Speziale and by Wieland, were talking about.

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

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

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

Right now I am keenly interested in identifying and focusing on the handful of new developments that could contribute to a nearterm reformulation of the theory. These are the things I expect to figure significantly in the Loops 2013 conference at Perimeter. Here is a checklist of short names--to help us (or at least me) keep them all in mind. All five bear watching:

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

These are abbreviated names so you and I can review the checklist in our minds without stumbling over a lot of of extra syllables. what they refer to is spelled out in more detail a few posts back in this thread, and links to sample research papers are given. For instance look back to post #117

 

[marcus]

Gene Bianchi gives an important seminar talk tomorrow 16 October. It will be online.
http://relativity.phys.lsu.edu/ilqgs/
BTW He was recently awarded a Banting fellowship at Perimeter, which made the Perimeter website front page :-D
Tomorrow's talk is Horizon entropy from loop gravity

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

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

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

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

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

To make it clearer to anyone new, I'll give a sample recent paper in each topic:

• PhenoCosmo http://arxiv.org/abs/1209.1609
• Group-tagged foam http://arxiv.org/abs/1208.3388
• Black holes where G and gamma run http://arxiv.org/abs/1210.2252
• Relistic Stat Mech and Thermo http://arxiv.org/abs/1209.0065
• Twistor Loop Tensor Group http://arxiv.org/abs/1207.6348

 

[marcus]

Bianchi's talk is online.
Slides: http://relativity.phys.lsu.edu/ilqgs/bianchi101612.pdf
Audio: http://relativity.phys.lsu.edu/ilqgs/bianchi101612.wav

 

[marcus]

Sample of recent Perimeter talks ( http://pirsa.org ) relevant to the current QG directions, now online:

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

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

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

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

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

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

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

 

[marcus]

Bee Hossenfelder has a summary of the recent conference (Experimental Search for Quantum Gravity) at her blog.
http://backreaction.blogspot.com/2012/10/esqg-2012-conference-summary.html

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

Simone Speziale is up next, in one week (6 November)
Twistorial structure of loop quantum gravity transition amplitudes

 

[marcus]

As context to the Carrozza seminar talk today, here is an October 1 post of mine.

I completely overlooked an important paper! It feeds into a potential near term reformulation of LQG. It is by Carrozza, Oriti, and Rivasseau about Tensorial GFT.
I should have had this paper on the 3rd quarter MIP poll (it came out in July) and somehow missed it.

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

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

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

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

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

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

Renormalization of Tensorial Group Field Theories
http://relativity.phys.lsu.edu/ilqgs/carrozza103012.pdf
http://relativity.phys.lsu.edu/ilqgs/carrozza103012.wav
The talk is good and there is extensive questioning and discussion by Joseph Ben Geloun, Lee Smolin, Laurent Freidel, Carlo Rovelli, Abhay Ashtekar, Daniele Oriti and I believe others whose names I didn't catch.

 

[marcus]

If it turns out (as judging from the interest in Carrozza Oriti Rivasseau's paper it conceivably might) that TGFT (tensorial group field theory) serves as basis for a nearterm reformulation of LQG/SF, then those who wish to follow what is going on in the field could find this tutorial by Krajewski useful:
http://arxiv.org/abs/1210.6257
Group field theories
Thomas Krajewski
(Submitted on 23 Oct 2012)
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field theories, merging ideas from tensor models and loop quantum gravity. This lecture is organized as follows. In the first section, we present basic aspects of quantum field theory and matrix models. The second section is devoted to general aspects of tensor models and group field theory and in the last section we examine properties of the group field formulation of BF theory and the EPRL model. We conclude with a few possible research topics, like the construction of a continuum limit based on the double scaling limit or the relation to loop quantum gravity through Schwinger-Dyson equations
58 pages, Lectures given at the "3rd Quantum Gravity and Quantum Geometry School", March 2011, Zakopane

 

[marcus]

For several reasons I think this paper represents a critical development in the emerging reformulation that I'm trying to understand
http://arxiv.org/abs/1210.0418
Interpretation of the triad orientations in loop quantum cosmology
Claus Kiefer, Christian Schell
(Submitted on 1 Oct 2012)
Loop quantum cosmology allows for arbitrary superpositions of the triad variable. We show here how these superpositions can become indistinguishable from a classical mixture by the interaction with fermions. We calculate the reduced density matrix for a locally rotationally symmetric Bianchi I model and show that the purity factor for the triads decreases by decoherence. In this way, the Universe assumes a definite orientation.
12 pages, 1 figure

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

We can see signs of this shift (in how things are formulated) appearing in LQG, in other papers. But this is the first time I'm aware of it's happening in the Cosmology application LQC.

 

[marcus]

As a reminder, here are a half-dozen research areas where this approach to Quantum Gravity is being reshaped. All the ILQGS talks mentioned are now online with the sole exception of Bianca Dittrich's scheduled for 27 November.

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

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

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

I recently added the Kiefer and Schell paper http://arxiv.org/abs/1210.0418 as an indication of where that is going. Kiefer Schell have the purity/mixedness of quantum states run on a continuum from zero to one. A state is a trace-class operator ρ on the hilbert space, a generalized "density matrix". Pure states are those for which tr(ρ²) = 1, a kind of "purity index". As these gradually decohere, the purity index comes down from 1 to zero. In Kiefer Schell's case the quantum state of geometry does this as it interacts with the matter in the environment. If I'm not mistaken, LQG dynamics will be extended to include states of this density matrix ρ type (as Kiefer and Schell do with LQC) and Rovelli's September paper is a step in this direction. Then the problem will be to understand how the purity index of the state is driven *up* during bounce. Intuitively there is a "release of information" when Planckian density density is approached, and information that had become inaccessible becomes accessible (in the repellent gravity phase of the bounce.) I could of course have this wrong, so I'm looking for other viewpoints.

 

[marcus]

Let's just look at the last 4 of the above LQG initiatives. HSF answers criticism by Alexandrov, so we can disregard the latter.
holonomySF (Hellmann's ILQGS talk and 1208.3388)
See Hellmann's comment here:
https://www.physicsforums.com/showthread.php?p=4162474#post4162474
(If anyone is new to the discussion, Frank Hellmann posts here as f-h.)
Dittrich may have some more to say about holonomy spin foam models in her ILQGS talk on 27 November.
============
The main thing I have to say right now is that in a certain sense all of the last three are working towards the same goal. The point is that a thermal state automatically breaks Lorentz invariance e.g. page 18 of Connes Rovelli gr-qc/9406019. So it is a no-brainer that any thermal state would have its own inherent notion of time. The challenge is to realize this in GR, what is a thermal state in GR which is timeless?
If one can do that, one finesses "dust". Thermal time and dust are reading from the same page of the book.
dust (Wise's ILQGS talk and 1210.0019)
hybrid LQC
An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era (1211.1354)
The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations (in prep)
GR Thermo and C*-algebra
General relativistic statistical mechanics (1209.0065)
Horizon entanglement entropy and universality of the graviton coupling (Bianchi's ILQGS talk and 1211.0522)
Interpretation of the triad orientations in loop quantum cosmology (1210.0418)

And hybrid LQC (the breakground work of Agullo Ashtekar Nelson) is a way of putting an infinity of DoF into LQG cosmology, around the time of the bounce before conventional inflation begins. This gives a way to grasp the thermal state. So these three things are, I think, aimed at one goal.

 

[marcus]

In two days Dittrich will give an online ILQGS talk, the last one of the fall semester.

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

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

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

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

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

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

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

If I had to bet now concerning the future course of LQG development---near future, see where we are in July 2013---I think I would say, as of now, that the two most interesting lines of development are HSF and a nexus of ideas I would call
"GR thermo, C*-algebra, hybrid LQC"
I see these things as coming together and clarifying, among other things, the LQC bounce (which is where the opening to phenomenology seems to be IMHO). Hybrid LQC puts Fock into the bounce picture--lots of particles and geometric fluctuations. (See latest Agullo Ashtekar Nelson.)
The C*-algebra formalism gives a way to do general covariant statistical quantum mechanics. (See new version of http://arxiv.org/abs/1209.0065 that was uploaded 19 November with a new section (Appendix B4) at the end with title something like "GC statistical QM".

 

[marcus]

The slides PDF for Dittrich's talk is already online.
http://relativity.phys.lsu.edu/ilqgs/dittrich112712.pdf
It's about Coarse Graining spinfoam QG and spin net etc. and it is an exceptionally
clear set of slides. Refers to a lot of work in progress (w.i.p.) and recent papers.
Try here http://relativity.phys.lsu.edu/ilqgs/ later in the day to see if audio is online.

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

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

The type of spinfoam they use is HSF (holonomy sf) and the 2D analog of that is what they call spin net. Both have group element labels rather than some other kind (e.g. spins, twistors). But much of the work involves highly simplified toy models. Not QG. Regular lattices. This does not mean it's trivial or uninteresting! On the contrary, I would say. It looks to me as if an effective method of coarsegraining for 4D spinfoam QG is being developed, and one that can be implemented numerically. If that is the case it will be a substantial advance.

 

[marcus]

I need to elaborate the nexus of ideas mentioned in posts #130 and 131 that seem to be coming to a better understanding of the LQC bounce.
"GR thermo, GC statistical QM, hybrid LQC, pre-inflationary dynamics, matter bounce"

Holonomy spinfoam models are a different kind of spinfoam, similar to lattice connection theories in that they use group element labels living on the 2-complex...
...I gather from comments made that people working on HSF (coarse graining, asymptotics, dynamics...) have indicated they see the approach as overcoming some obstacles/unresolved questions in the earlier version of spinfoam.
...
If I had to bet now concerning the future course of LQG development---near future, see where we are in July 2013---I think I would say, as of now, that the two most interesting lines of development are HSF and a nexus of ideas I would call
"GR thermo, C*-algebra, hybrid LQC"
I see these things as coming together and clarifying, among other things, the LQC bounce (which is where the opening to phenomenology seems to be IMHO). Hybrid LQC puts Fock into the bounce picture--lots of particles and geometric fluctuations. (See latest Agullo Ashtekar Nelson.)
The C*-algebra formalism gives a way to do general covariant statistical quantum mechanics. (See new version of http://arxiv.org/abs/1209.0065 that was uploaded 19 November with a new section (Appendix B4) at the end with title something like "GC statistical QM".

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

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

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

*Nelson was at PennState and is now at Nijmegen, he also gave a talk at the Stockholm cosmology conference.

 

[marcus]

Classical/semiclassical corroboration--chaos, volume gap

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

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

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

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

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

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

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

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

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

In case anyone is interested in Berndt Müller's earlier research interests http://inspirehep.net/author/B.Muller.1/

 

[marcus]

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

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

I continue to be impressed by how many active directions of research in LQG there are at present. I listed some of them a few posts back. I suspect the map of LQG is going to be quite different in July when Loops 2013 is held, from what it was at the previous Loops conference held in 2011 at Madrid.
http://www.perimeterinstitute.ca/conferences/loops-13

 

[marcus]

Is it possible that Mielczarek is on to something? Can we give meaning to what he says here which seems so incomprehensible the first time I read it?
At Planck scale, or thereabouts, the spacetime causal structure would be numbed as if by a massive shot of novocaine, into non-existence. All lines of communication go dead?

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

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

I would like to dismiss this as too far-out, but don't feel that I can. LQG research is going in a bewildering variety of different directions right now. I don't remember it ever being so multi pronged in past years.

 

[marcus]

I'll recall post #129 at the top of this page, just so we don't get so intrigued by detail that we lose track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference (Loops 13 July of next year).

As a reminder, here are a half-dozen research areas where this approach to Quantum Gravity is being reshaped.

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

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

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

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

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

In the the entanglement entropy part of above post, I added a reference (in red) to a new paper by Bianchi and Myers:
http://arxiv.org/abs/1212.5183
On the Architecture of Spacetime Geometry
Eugenio Bianchi, Robert C. Myers
(Submitted on 20 Dec 2012)
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein-Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity and loop quantum gravity, as well as the AdS/CFT correspondence.
8 pages, 1 figure

 

[marcus]

The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

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

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

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

It's hard to know what to call the next development. Perhaps "C*-quantum gravity, T-time, and entanglement entropy".
Work towards general covariant (GC) analysis such as GC-thermo, GC statistical (quantum) mechanics seems to motivate an (M,ω) formulation. This finally solves the time problem because one gets an observer-independent (Tomita) flow on the observables algebra. But how do we recover the regional STRUCTURE of space in the (M,ω) context? I see Bianchi Myers paper in this light. The key word "architecture" in the title is a signal. Also Kiefer Schell paper leans in that direction.
C*-quantum gravity, T-time, entanglement
Rovelli—General relativistic statistical mechanics (http://arxiv.org/abs/1209.0065)
Bianchi—Horizon entanglement entropy and universality of the graviton coupling (ILQGS talk and http://arxiv.org/abs/1211.0522)
Bianchi Myers—On the Architecture of Spacetime Geometry (http://arxiv.org/abs/1212.5183)
Kiefer Schell—Interpretation of the triad orientations in loop quantum cosmology (http://arxiv.org/abs/1210.0418)
Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)

 

[marcus]

The ILQGS (international LQG seminar) is a good pointer to active areas of QG research---one can see this in the previous post: several of the themes we identified were represented not only by recent papers but also by Fall 2012 semester talks. Jorge Pullin organizes the ILQGS and I think he does a great job.

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

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

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

Others of the talks are on topics that feature in our 4th quarter MIP poll. I have to go---there's more to say about this.

 

[marcus]

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

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

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

So later this month, as 29 January approaches, some of us will probably decide to take a look at the November paper to prepare for listening to the online seminar titled:
Entanglement in loop quantum gravity by Eugenio Bianchi.

 

[marcus]

The idea of this thread is to keep track of the full spectrum of different ways QG is being reshaped in the runup to the main QG conference http://www.perimeterinstitute.ca/conferences/loops-13 (Loops 13 at Perimeter Institute in July 2013).

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

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

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

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

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

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

Besides the above there are several other clear reformulation initiatives under way.
twistorLQG (Speziale's ILQGS talk and http://arxiv.org/abs/1207.6348)
tensorialGFT (Carrozza's ILQGS talk and http://arxiv.org/abs/1207.6734)
holonomySF (Hellmann's ILQGS talk and http://arxiv.org/abs/1208.3388)
dust (Wise's ILQGS talk and http://arxiv.org/abs/1210.0019)

 

[marcus]

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

To get a sense of Wieland you could watch some of this Perimeter talk (February 2012):
http://pirsa.org/12020129/

 

[marcus]

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

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

If one is rereading the papers in order to prepare to understand the online talk, there is also Bianchi's December paper with Rob Myers (http://arxiv.org/abs/1212.5183) which I mentioned two posts back.

 

[MTd2]

The twistorial reformulation of LQG has taken a big step forward with:

I think it should be remarked that this time time is only a dimension like in GR.

 

[marcus]

Bianchi's slides http://relativity.phys.lsu.edu/ilqgs/bianchi012913.pdf are exceptionally clear, visual, and conceptually intuitive.
"Entanglement and the Bekenstein-Hawking entropy"
The B-H entropy is explained simply as the entang. entropy between the two regions

It concludes with the Bianchi-Myers conjecture, which remains a conjecture (quite an interesting one.)

I just checked the audio link http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav and that part is not yet online.

 

[marcus]

The audio for Bianchi's 29 Jan ILQGS talk has been posted:
http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav

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

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

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

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

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

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

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

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

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

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

http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

 

[marcus]

The papers of Engle and by Alesci Cianfrani mentioned in above post indicate that Loop cosmology can be embedded in the full LQG theory, or derived from it. Reductions to the interesting cases for cosmology can be done AFTER the quantum theory is constructed. It has been pointed out that this opens the way for testing the full LQG theory. It has to give the right answers about the early universe.

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

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

 

[tom.stoer]

Marcus, what about some kind of "status report" of LQG?

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

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

 

[marcus]

Marcus, what about some kind of "status report" of LQG?

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

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

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

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

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

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

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

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

This is why I think it is so important to review Marciano's May 2012 talk, and to hear Alexander's talk tomorrow (26 February 2013).

 

[marcus]

As I see it, LQG is a subfield of LQC. Much (perhaps most) Loop community work is now Cosmo-related. Papers by Engle and by Alesci show a good bridge, symmetry reduction can be done at the quantum level. And symmetry restrictions are gradually being relaxed--eg the work on Bianchi-One cosmologies.

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

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

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

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

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

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

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

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

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

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

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