Reformulation of Loop gravity in progress, comment?

marcus

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

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/201...e-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.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:
http://physicsforums.com/showthread....74#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"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

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 Lifshitz (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.