Reformulation of Loop gravity in progress, comment?

[tom.stoer]

It's especially the math like the f-map which makes the 3+1 stuff so special. I have to check Thiemann's papers on LQG+SUGRA etc. He states ants to study LQG in arbitary dimensions, so he must have found a way to get rid of these special properties of 3+1 dim Riemannian manifolds and SL(2,C).

 

[marcus]

I want to look now at a different direction (or perhaps it is related) that the reformulation of LQG could go, over the next year or two. This is indicated by the Gielen Wise paper on the current MIP poll.

In this paper the authors work with the concepts of "field of observers" and "space of observers". I see this as part of an historical process of the subjectification of spacetime. It is related to the research at Perimeter Institute concerning "Principle of Relative Locality". To me personally, what Gielen Wise are talking about it more interesting than "Relative Locality", and may contain it. But this may simply be arbitrary preference on my part.

Here's the latest one:
http://arxiv.org/abs/1206.0658
Linking Covariant and Canonical General Relativity via Local Observers
Steffen Gielen, Derek K. Wise

In this, Gielen and Wise say they have in preparation a new paper called
Lifting general relativity to observer space

So we will see how soon that one comes out and what, if any, impact it has. Last year the authors posted a couple of papers on this general subject:

http://arxiv.org/abs/1111.7195/
Spontaneously broken Lorentz symmetry for Hamiltonian gravity
Steffen Gielen, Derek K. Wise
http://arxiv.org/abs/1112.2390
The geometric role of symmetry breaking in gravity
Derek K. Wise

 

[marcus]

Some thoughts in back of mind about this: a projectile doesn't HAVE a continuous trajectory.
You can't monitor it along an infinite number of points. You just have a finite series of places you know it's been. A continuous traj. for the projectile doesn't EXIST in nature.
(you can't tell which slit it went thru unless you monitored there.)

A spacetime is like a trajectory. So spacetime does not exist in nature. The universe doesn't HAVE a continuous spacetime geometry.

There are kind of two responses that I see:
1. Hartle's new standard QM. You can partition the histories according to a finite number of factual questions. Some partitions will be sufficiently uncorrelated that you can assign odds and make bets (predictions) and settle bets. No essential role for any observer.
(Of course there is no fundamental space time either. It does not exist in the theory, except as a low energy approximation. Conventional spacetime geometry "emerges" under appropriately "tame" conditions from the more primitive Q&A of Hartle's decoherent partitions of the set of possible histories.

2. Gielen and Wise's response, which I'm still vague about. Instead of fashioning a mathematical model of spacetime geometry (which doesn't exist, that's the problem) you construct a mathematical model of the space of observers which they claim is 7 dimensional. On the face of it, it sounds strange. But I think it's probably worth having a look. In any case, I posted the links to their papers.

 

[marcus]

We know there is some interest in joining LQG with the Hartle "Histories" approach to Quantum Mechanics--at least one grad student working on this. So it makes sense to keep that in our field of vision.

In that connection, Fay Dowker is giving a talk at Perimeter on Tuesday about the Histories approach and in particular how one can recover the Hilbert state space of older QM (under certain assumptions) starting from a PoV in which Histories, not states, are fundamental.
She seems to be one of the main people developing the approach that Hartle initiated.

The talk will probably be based on two 2010 papers. I will get the links:
http://arxiv.org/abs/1002.0589
Hilbert Spaces from Path Integrals
Fay Dowker, Steven Johnston, Rafael D. Sorkin
(Submitted on 2 Feb 2010)
It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown that the History Hilbert space is the standard Hilbert space in the case of non-relativistic quantum mechanics.
22 pages.

http://arxiv.org/abs/1007.2725
On extending the Quantum Measure
Fay Dowker, Steven Johnston, Sumati Surya
(Submitted on 16 Jul 2010)
We point out that a quantum system with a strongly positive quantum measure or decoherence functional gives rise to a vector valued measure whose domain is the algebra of events or physical questions. This gives an immediate handle on the question of the extension of the decoherence functional to the sigma algebra generated by this algebra of events. It is on the latter that the physical transition amplitudes directly give the decoherence functional. Since the full sigma algebra contains physically interesting questions, like the return question, extending the decoherence functional to these more general questions is important. We show that the decoherence functional, and hence the quantum measure, extends if and only if the associated vector measure does...
23 pages, 2 figures

And here is the link for the PIRSA video of next week's (10 July) seminar talk:
http://pirsa.org/12070001/
The Path Integral Interpretation of Quantum Mechanics
Speaker(s): Fay Dowker
Abstract: In 1932 Dirac wrote that the lagrangian approach to classical mechanics was probably more fundamental than the hamiltonian approach because the former is relativistically invariant whereas the latter is "essentially nonrelativistic". In quantum theory the hamiltonian approach leads to canonincal quantisation, Hilbert space, operators and the textbook rules for state vector "collapse", which are all indeed more or less divorced from the spacetime nature of the physical world as revealed by relativity. The "essentially relativistic" lagrangian approach on the other hand leads to the path integral, as shown by Dirac in 1932 and developed by Feynman. I will show how the interpretation of quantum mechanics in a path integral framework is based directly on events in spacetime and show that it leads to a second "fork in the road" depending on whether it is necessary for probabilities to play a fundamental role in the theory.
Date: 10/07/2012 - 3:30 pm

I suspect that the "second fork in the road" is where one decides whether or not to make an additional assumption (may allow one to recover effective use of the mathematical utilities of conventional state-space QM.)

 

[atyy]

@marcus, one of the things Rovelli likes to say is that time is emergent. In the histories formulation, isn't time primary?

I think Markopoulou has argued that time is primary, so maybe the histories formulation would be more compatible with her viewpoint?

Here's a Markopoulou paper that mentions "histories", but I'm not sure if it's related to Hartle's "histories": http://arxiv.org/abs/gr-qc/0703097

Ooops, from this review, I see the histories approach is Griffiths's!

 

[marcus]

In the case of Dowker's talk (and the tentative exploration of Hartle's QM that I've seen from Marseille) we are following a specific line of development. It might just be a distraction at this point to talk about Griffith's work in 1975, or Markopoulou (who means something else by "causal histories") or the Hohenberg review you linked, which does not use Hartle's terminology and is not focused on this specific line.

If anyone is interested in understanding the significance of Dowker's talk, I would suggest studying Hartle's 2006 paper, that was presented at the 23rd Solvay Conference---whose theme was "The Quantum Structure of Space and Time". Hartle's paper sets out axioms for the decoherence functional which is basic to his particular Histories approach. Of course he acknowledges Griffiths 1975 work but that's ancient history.
I've looked over a bunch of papers and this is a key one:

http://arxiv.org/abs/gr-qc/0602013
Generalizing Quantum Mechanics for Quantum Spacetime
James B. Hartle (University of California, Santa Barbara)
(Submitted on 2 Feb 2006)
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value. This paper reviews a fully four-dimensional, sum-over-histories, generalized quantum mechanics of cosmological spacetime geometry. This generalization is constructed within the framework of generalized quantum theory. This is a minimal set of principles for quantum theory abstracted from the modern quantum mechanics of closed systems, most generally the universe. In this generalization, states of fields on spacelike surfaces and their unitary evolution are emergent properties appropriate when spacetime geometry behaves approximately classically. The principles of generalized quantum theory allow for the further generalization that would be necessary were spacetime not fundamental...
31 pages. 4 figures.

To paraphrase, states and evolution of fields defined on spacelike surfaces are ONLY appropriate as math idealizations when geometry behaves APPROXIMATELY CLASSICALLY. In more general situations such idealizations are NOT appropriate.
They are, as Dowker puts it in her seminar talk abstract, "more or less divorced from the spacetime nature of the physical world".

 

[atyy]

So is time fundamental in Dowker's approach?

The Hartle paper has a beautiful quote: ‘Traveler, there are no paths, paths are made by walking.’ It's also interesting that David Gross delivered Hartle's talk.

 

[marcus]

So is time fundamental in Dowker's approach?

The Hartle paper has a beautiful quote: ‘Traveler, there are no paths, paths are made by walking.’ It's also interesting that David Gross delivered Hartle's talk.

There is no time. Time is made by histories
As I recall, David Gross was the chairman and main organizer of the 23rd Solvay.
He would have decided the theme "The Quantum Structure of Space and Time" and, I guess,
invited Hartle to contribute a paper. For whatever reason, Hartle was unable to make it to the conference and so the paper was presented in his stead.

If anyone is interested in watching, last year Hartle gave a talk at Perimeter on related matters. Here's a video:
http://pirsa.org/11020124/
Quantum Mechanics with Extended Probabilities
Speaker(s): James Hartle
Abstract: We present a new formulation of quantum mechanics for closed systems like the universe using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for alternative histories that are the basis of settleable bets. However, quantum mechanics describes alternative histories are not the basis for settleable bets as in the two-slit experiment. These alternatives can be assigned extended probabilities that are sometimes negative. We will compare this with the decoherent (consistent) histories formulation of quantum theory. The prospects for using this formulation as a starting point for testable alternatives to quantum theory or further generalizations of it will be briefly discussed.
Date: 07/03/2011 - 11:00 am
Here's another, but not so recent:
http://pirsa.org/07090064/

 

[atyy]

In Dowker's http://arxiv.org/abs/1002.0589 section 3.2, it looks like time is fundamental for defining a history.

 

[atyy]

The Dowker talk abstract says something about a deterministic versus probabilistic formulation. Is that in her published work, or is that new?

 

[marcus]

In Dowker's http://arxiv.org/abs/1002.0589 section 3.2, it looks like time is fundamental for defining a history.

I don't see any evidence of that. At the beginning of section 3 they say plainly that they are considering a special case. And a time variable IS employed in that setup.

Throughout the paper they are building bridges and comparisons between their Histories approach and conventional QM, especially the example of a conventional non-relativistic particle moving in d-dimensional Euclid space according to a conventional clock. They are interested in showing that their theoretical framework can handle that and get the same results as the conventional one.

So in that paper they are always studying examples in which there IS time. But time does not appear in their axioms. So I think you are mistaken about it looking like it's fundamental.

 

[marcus]

...here is the link for the PIRSA video of next week's (10 July) seminar talk:
http://pirsa.org/12070001/
The Path Integral Interpretation of Quantum Mechanics
Speaker(s): Fay Dowker
Abstract: In 1932 Dirac wrote that the lagrangian approach to classical mechanics was probably more fundamental than the hamiltonian approach because the former is relativistically invariant whereas the latter is "essentially nonrelativistic". In quantum theory the hamiltonian approach leads to canonincal quantisation, Hilbert space, operators and the textbook rules for state vector "collapse", which are all indeed more or less divorced from the spacetime nature of the physical world as revealed by relativity. The "essentially relativistic" lagrangian approach on the other hand leads to the path integral, as shown by Dirac in 1932 and developed by Feynman. I will show how the interpretation of quantum mechanics in a path integral framework is based directly on events in spacetime and show that it leads to a second "fork in the road" depending on whether it is necessary for probabilities to play a fundamental role in the theory.
Date: 10/07/2012 - 3:30 pm
...

The Dowker talk abstract says something about a deterministic versus probabilistic formulation. ...

I think you are mistaken. There is no reference to "deterministic" in the abstract. I think you are probably reading too much into the abstract, or putting your own interpretation on it.

When one is constructing a non-deterministic theory one does not automatically get probabilities (numbers between zero and one satisfying certain laws). It may require additional stronger assumptions in order to make probabilities play a fundamental role.

 

[marcus]

Anyway the way I see it we are in an exciting moment for Loop gravity. There are all these developments that could feed into a reformulation that shows up as early as July 2013 with the Warsaw GR20, or at Perimeter's Loops 2013 conference.

A.Stacking Spin Networks (systematically to generate spin foams)
http://arxiv.org/abs/1107.5185
Feynman diagrammatic approach to spin foams
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta
(Submitted on 26 Jul 2011)

B.Histories
http://arxiv.org/abs/gr-qc/0602013
Generalizing Quantum Mechanics for Quantum Spacetime
James B. Hartle (University of California, Santa Barbara)
(Submitted on 2 Feb 2006)
and currently
http://pirsa.org/12070001/
The Path Integral Interpretation of Quantum Mechanics
Fay Dowker
10 Jul 2013

C. Unclamping the Immirzi
http://arxiv.org/abs/1204.5122
Entropy of Non-Extremal Black Holes from Loop Gravity
Eugenio Bianchi
(Submitted on 23 Apr 2012)

D. Using the tetrad's sign
http://arxiv.org/abs/1205.0733
Discrete Symmetries in Covariant LQG
Carlo Rovelli, Edward Wilson-Ewing
(Submitted on 3 May 2012)

E. Thermodynamics
http://arxiv.org/abs/1204.6349
Gravitation and vacuum entanglement entropy
Ted Jacobson
(Submitted on 28 Apr 2012)
http://arxiv.org/abs/1205.5529
General relativity as the equation of state of spin foam
Lee Smolin
(Submitted on 24 May 2012)
http://arxiv.org/abs/1207.0505
Emergent perspective of Gravity and Dark Energy
T. Padmanabhan
(Submitted on 2 Jul 2012)

F. Dust. Actual Hamiltonians (instead of constraints.)
http://arxiv.org/abs/1206.3807
Scalar Material Reference Systems and Loop Quantum Gravity
Kristina Giesel, Thomas Thiemann
(Submitted on 17 Jun 2012)
http://arxiv.org/abs/1206.0658
Linking Covariant and Canonical General Relativity via Local Observers
Steffen Gielen, Derek K. Wise
(Submitted on 4 Jun 2012)

 

[marcus]

Fay Dowker has now given her seminar talk at Perimeter and the video version is already posted here:
http://pirsa.org/12070001

As I said, I see some 6 main ideas that could enter into Loop gravity and change how it is formulated. I can't talk probabilities as I'm just an interested observer, not an expert. These ideas are one the scene and some (or none!) might affect the theory. Because there are so many balls in the air, I boiled them down to 6 keywords to make them easier to recall.

Stacking
Histories
Unclamping
Tetrad
Thermo
Dust

Stacking refers to Lewandowski group's way to systematically ENUMERATE and compute spinfoam histories. They stack up successive spin network states of geometry and join them into a single history.

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

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

The Tetrad's sign could be included in the classical theory upon which Loop gravity is based. Papers by Rovelli and others raise the issue: should the sign be included? If so, in which of two possible ways? How would this affect the quantum theory?

Thermodynamics of geometry is the theme of some recent papers by Jacobson, Smolin, Padmanabhan and others. Could the Einstein GR equation be (like PV = NkT) the equation of state describing overall behavior of microscopic variables (like the vast number of gas molecules whose collective behavior is summarized by PV = NkT.) If GR is the equation of state, what are the underlying degrees of freedom? Do spinfoams describe the underlying degrees of freedom for which EFE is the EoS?

Dust is shorthand for the various approaches being used to recover a real physical Hamiltonian. Members of both the Erlangen and Warsaw groups have research along several related lines. This is familiar from cosmology and I think it's of considerable practical value. It's the one thing I feel sure will be prominently featured in Loops 2013 and next year's GR20 conference in Warsaw.

 

[marcus]

Dowker gave an impressive talk.
It helps if you download the slides PDF first (which takes me about 3 minutes):
http://pirsa.org/pdf/loadpdf.php?pirsa_number=12070001
Then scroll thru the slides while watching the video.
http://pirsa.org/12070001
There is a lot on the slides and their video images are not as legible as the PDF.

She presents Sorkin (and her) QUANTUM MEASURE THEORY as a rival alternative to Hartle's DECOHERENT HISTORIES. Both are proposed histories formulations of QM.
As she presents it, QMT is still being worked out. She also points to a drawback in Hartle's DH approach.

This seems compatively mild to me: it is that there are different ways of partitioning the set of all histories so you get approximate decoherence and additive probabilities. She refers to this as something you have to "struggle with" in the Hartle approach.

But the struggle seems more serious if the probability addition rule is relaxed and all you require is "preclusion" (that events with measure subjectively considered to be very small do not occur.) The preclusion approach is what she and Sorkin are working on. She gave two examples showing a grave contradiction in this approach, where you do not require additive probabilities. In these examples no single history could occur because each one was contained in a subset of measure zero. One example, starting at minute 60, was a variant of the GHZ construction--Greenberger, Horne, and Zeilinger--may be familiar to some.
(e-copy of original GHZ 1998 paper: http://arxiv.org/abs/0712.0921 "Going Beyond Bell's Theorem")

 

[marcus]

Prompted by Dowker's talk, I am trying to assess how serious the problems are with Hartle's Decoherent Histories QM.
Here are some papers by Adrian Kent discussing the problem that decoherent partitions are not unique, and (as of 1994 and 1996 according to Kent) can lead to contradictory predictions. I don't know if the problems alleged by Kent are real or if they have been fixed since then.

Hartle's 2006 paper for the 23rd Solvay Conference proceedings does not cite Kent and does not seem to answer his criticisms, which is puzzling.
http://arxiv.org/abs/gr-qc/9809026
Quantum Histories
http://arxiv.org/abs/gr-qc/9808016
Consistent Sets and Contrary Inferences: Reply to Griffiths and Hartle
http://arxiv.org/abs/gr-qc/9607073
Quantum Histories and Their Implications
http://arxiv.org/abs/gr-qc/9604012
Consistent Sets Yield Contrary Inferences in Quantum Theory
http://arxiv.org/abs/gr-qc/9412067
On the Consistent Histories Approach to Quantum Mechanics

However I see that Griffiths and Hartle did reply to Kent's crit here:
http://arXiv.org/abs/gr-qc/9710025
Comment on "Consistent Sets Yield Contrary Inferences in Quantum Theory''
Robert B. Griffiths (Carnegie-Mellon University), James B. Hartle (University of California, Santa Barbara)
(Submitted on 3 Oct 1997)
In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can be inferred with probability one, and such that the projectors representing these two propositions are mutually orthogonal. In this note we stress that, according to the rules of consistent history reasoning two such propositions are not contrary in the usual logical sense namely, that one can infer that if one is true then the other is false, and both could be false. No single consistent family contains both propositions, together with the initial and final states, and hence the propositions cannot be logically compared. Consistent histories quantum theory is logically consistent, consistent with experiment as far as is known, consistent with the usual quantum predictions for measurements, and applicable to the most general physical systems. It may not be the only theory with these properties, but in our opinion, it is the most promising among present possibilities.
2 pages

 

[marcus]

Loops 2013 conference will be held July 22-26 next year at Perimeter Institute and it's interesting to try to identify now what new ideas and developments could enter into the formulation of Loop quantum geometry/gravity/cosmology that we'll see set out a year from now, at conference.
I should probably update my list of ideas I'm guessing could enter significantly into the picture. There are now 7 of them.
Stacking
Histories
Unclamping
Tetrad-sign
Thermo
Dust
Higgsflation

Stacking refers to Lewandowski group's way to systematically ENUMERATE and compute spinfoam histories. They stack up successive spin network states of geometry and join them into a single history.
http://arxiv.org/abs/1107.5185

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

Unclamping the Immirzi parameter was a consequence of Bianchi's black hole entropy result S=A/4. It appears to me to have exciting and unpredictable implications for the theory.
http://arxiv.org/abs/1204.5122

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

Thermodynamics of geometry is the theme of some recent papers by Jacobson, Smolin, Padmanabhan and others. Could the Einstein GR equation be (like PV = NkT) the equation of state describing overall behavior of microscopic variables (like the vast number of gas molecules whose collective behavior is summarized by PV = NkT.) If GR is the equation of state, what are the underlying degrees of freedom? Do spinfoams describe the underlying degrees of freedom for which EFE is the EoS?
http://arxiv.org/abs/1204.6349 http://arxiv.org/abs/1205.5529 http://arxiv.org/abs/1207.0505

Dust is shorthand for the various approaches being used to recover a real physical Hamiltonian. Members of both the Erlangen and Warsaw groups have research along several related lines. This is familiar from cosmology and I think it's of considerable practical value.
http://arxiv.org/abs/1206.3807 http://arxiv.org/abs/1206.0658

Higgs inflation in Loop cosmology is the topic of a new paper by three young researchers that just appeared and impressed me as potentially important. It's by Tom Pawlowski, a postdoc at Warsaw, and two PhD students there: Andrea Dapor and Michal Artymowski.
It puts inflation in a new light for me. So I expect some rapid development in this area:
http://arxiv.org/abs/1207.4353
Inflation from non-minimally coupled scalar field in loop quantum cosmology
Michal Artymowski, Andrea Dapor, Tomasz Pawlowski
(Submitted on 18 Jul 2012)
The FRW model with non-minimally coupled massive scalar field has been investigated in LQC framework. Considered form of the potential and coupling allows applications to Higgs driven inflation. The resulting dynamics qualitatively modifies the standard bounce paradigm in LQC in two ways: (i) the bounce point is no longer marked by critical matter energy density, (ii) the Planck scale physics features the "mexican hat" trajectory with two consecutive bounces and rapid expansion and recollapse between them. Furthermore, for physically viable coupling strength and initial data the subsequent inflation exceeds 60 e-foldings.
14 pages, 5 figures
I should give links to earlier papers by Bezrukov and Shaposhnikov
http://arxiv.org/abs/0710.3755 (209 cites)
The Standard Model Higgs boson as the inflaton
http://arxiv.org/abs/0904.1537 (78 cites)
Standard Model Higgs boson mass from inflation: two loop analysis
The latter was cited by ADP.

 

[marcus]

The Loops conference is biennial, every two years. The previous one, Loops 2011 was held in Madrid. Videos of many of the talks, and PDF files of slide presentations are online here:
http://www.iem.csic.es/loops11/ (click on the Scientific Program menu item)
Loops 2013 conference starts just one year from today. It will be held July 22-26 next year at Perimeter Institute.

I've been trying to visualize what main topics and new developments might figure prominently at the next Loops conference. After thinking it over for several weeks and considering various alternatives I've come around, at least for now, to the belief that Loop cosmology will stand out and show the most active development. Particularly the phenomenology side of it where e.g. you model different types of BOUNCE and different mechanisms of INFLATION and you figure out what traces to look for in the ancient light of the Cosmic Background. Among other things gravitational waves would leave their imprint (magnified by expansion) on the microwave sky.

I think other major themes are going to be
DUST
INHOMOGENEITY

The Warsaw and Erlangen people have been working hard on a straightforward Hamiltonian operator-based Loop program and they sound like they think they've succeeded. Lewandowski says we now have Quantum Gravity. So that puts a new light on the situation. It uses a matter field (uniform dust-like) but that is nothing new. Cosmology models have always had that convenience. I'm using "dust" as shorthand for the various approaches being used to recover a real physical Hamiltonian. This is familiar from cosmology and I think it's of considerable practical value.
http://arxiv.org/abs/1206.3807 http://arxiv.org/abs/1206.0658

And I keep seeing Loop cosmology papers with more and more non-uniformity, various "Bianchi" classes of messed up universes---bouncing nevertheless. That's a major trend in the program---generalizing LQC to remove the uniformity restriction and get increasingly realistic.
Inhomogeneity is the focus of this recent paper:
http://arxiv.org/abs/1204.1288
Perturbations in loop quantum cosmology
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 5 Apr 2012)
The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, Quantum Gravity, phase of the universe. Here we describe how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB.
4 pages ICGC (2011) Goa Conference proceedings

Higgs inflation in Loop cosmology is the topic of a new paper that just appeared and impressed me as potentially important. It's by Tom Pawlowski, a postdoc at Warsaw, and two PhD students there: Andrea Dapor and Michal Artymowski.
It puts inflation in a new light for me. So I expect some rapid development in this area:
http://arxiv.org/abs/1207.4353
Inflation from non-minimally coupled scalar field in loop quantum cosmology
Michal Artymowski, Andrea Dapor, Tomasz Pawlowski
(Submitted on 18 Jul 2012)
The FRW model with non-minimally coupled massive scalar field has been investigated in LQC framework. Considered form of the potential and coupling allows applications to Higgs driven inflation. The resulting dynamics qualitatively modifies the standard bounce paradigm in LQC in two ways: (i) the bounce point is no longer marked by critical matter energy density, (ii) the Planck scale physics features the "mexican hat" trajectory with two consecutive bounces and rapid expansion and recollapse between them. Furthermore, for physically viable coupling strength and initial data the subsequent inflation exceeds 60 e-foldings.
14 pages, 5 figures
Here are links to earlier papers by Bezrukov and Shaposhnikov
http://arxiv.org/abs/0710.3755 (209 cites)
The Standard Model Higgs boson as the inflaton
http://arxiv.org/abs/0904.1537 (78 cites)
Standard Model Higgs boson mass from inflation: two loop analysis
The latter was cited by ADP.
====================
I should look and see what recent Loop CosmoPheno papers have been highly cited lately and that could give ideas. This post gave some search links for cite-ranked listings:

...
Here's a link that gets (desy key) LQG and LQC papers that mostly have to do with pheno, i.e. with opportunities for TESTING.
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+INFLATION+OR+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+&FORMAT=www&SEQUENCE=citecount%28d%29
This ranks by cites and gets around 108 papers.

Let's restrict to ones that appeared 2009 or later:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29

This gets 59 papers. Again they are ranked by cites.
...
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+(dk+loop+space+and+(quantum+gravity+or+quantum+cosmology)+)+and+(gravitational+radiation+or+primordial+or+inflation+or+power+spectrum+or+cosmic+background)+and+date%3E2008&SEQUENCE=CITECOUNT(D)&SKIP=25
It only gets 57 of the 59 but works more reliably in some cases.

For sure Agullo Ashtekar Nelson is going to figure in conference and also Artymowski Dapor Pawlowski, I would expect. But those haven't been out long enough to be cited much, so they would not necessarily be spotted in this kind of listing. Let's see what Loop CosmoPheno papers are picked out, however:

Links don't always remain active. So I will copy off a few items from the top of the list.
1) Cosmological footprints of loop quantum gravity.
J. Grain, (APC, Paris & Paris, Inst. Astrophys.) , A. Barrau, (LPSC, Grenoble & IHES, Bures-sur-Yvette) . Feb 2009. (Published Feb 27, 2009). 7pp.
Published in Phys.Rev.Lett.102:081301,2009.
e-Print: arXiv:0902.0145 [gr-qc] (46)

3) Loop quantum cosmology and slow roll inflation.
Abhay Ashtekar, David Sloan, (Penn State U.) . Dec 2009. 8pp.
Published in Phys.Lett.B694:108-112,2010.
e-Print: arXiv:0912.4093 [gr-qc] (32)

4) Possible observational effects of loop quantum cosmology.
Jakub Mielczarek, (Jagiellonian U., Astron. Observ. & LPSC, Grenoble) . Aug 2009. (Published Mar 15, 2010). 11pp.
Published in Phys.Rev.D81:063503,2010.
e-Print: arXiv:0908.4329 [gr-qc] (26)

5) Big Bounce and inhomogeneities.
David Brizuela, Guillermo A.D Mena Marugan, Tomasz Pawlowski, (Madrid, Inst. Estructura Materia) . Feb 2009. 4pp.
Published in Class.Quant.Grav.27:052001,2010.
e-Print: arXiv:0902.0697 [gr-qc] (21)

6) Inflation in loop quantum cosmology: dynamics and spectrum of gravitational waves.
Jakub Mielczarek, (Jagiellonian U.) , Thomas Cailleteau, (LPSC, Grenoble) , Julien Grain, (Paris, Inst. Astrophys.) , Aurelien Barrau, (LPSC, Grenoble) . Mar 2010. (Published May 15, 2010). 11pp.
Published in Phys.Rev.D81:104049,2010.
e-Print: arXiv:1003.4660 [gr-qc] (21)

7) Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation.
J. Grain, (APC, Paris & Paris, Inst. Astrophys.) , A. Barrau, (LPSC, Grenoble & IHES, Bures-sur-Yvette) , A. Gorecki, (LPSC, Grenoble) . Apr 2009. (Published Apr 2009). 15pp.
Published in Phys.Rev.D79:084015,2009.
e-Print: arXiv:0902.3605 [gr-qc] (20)

8) Observational constraints on loop quantum cosmology.
Martin Bojowald, (Penn State U.) , Gianluca Calcagni, (Potsdam, Max Planck Inst.) , Shinji Tsujikawa, (Tokyo U. of Sci.) . IGC-11-1-1, AEI-2011-004, Jan 2011. (Published Nov 18, 2011). 4pp.
Published in Phys.Rev.Lett.107:211302,2011.
e-Print: arXiv:1101.5391 [astro-ph.CO] (20)

9) Observational constraints on a power spectrum from super-inflation in Loop Quantum Cosmology.
Masahiro Shimano, Tomohiro Harada, (Rikkyo U.) . Sep 2009. (Published Sep 15, 2009). 17pp.
Published in Phys.Rev.D80:063538,2009.
e-Print: arXiv:0909.0334 [gr-qc] (19)

10) Fully LQC-corrected propagation of gravitational waves during slow-roll inflation.
J. Grain, (Paris, Inst. Astrophys.) , T. Cailleteau, A. Barrau, A. Gorecki, (LPSC, Grenoble) . Oct 2009. (Published Jan 15, 2010). 9pp.
Published in Phys.Rev.D81:024040,2010.
e-Print: arXiv:0910.2892 [gr-qc] (17)

11) Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model.
L.J. Garay, (Madrid U. & Madrid, Inst. Estructura Materia) , M. Martin-Benito, G.A. Mena Marugan, (Madrid, Inst. Estructura Materia) . May 2010. (Published Aug 15, 2010). 16pp.
Published in Phys.Rev.D82:044048,2010.
e-Print: arXiv:1005.5654 [gr-qc] (17)

12) Tensor power spectrum with holonomy corrections in LQC.
Jakub Mielczarek, (Jagiellonian U.) . Feb 2009. (Published Feb 2009). 13pp.
Published in Phys.Rev.D79:123520,2009.
e-Print: arXiv:0902.2490 [gr-qc] (16)

13) Inflationary observables in loop quantum cosmology.
Martin Bojowald, (Penn State U.) , Gianluca Calcagni, (Potsdam, Max Planck Inst.) . AEI-2010-161, IGC-10-11-1, Nov 2010. 40pp.
Published in JCAP 1103:032,2011.
e-Print: arXiv:1011.2779 [gr-qc] (16)

14) Observational test of inflation in loop quantum cosmology.
Martin Bojowald, (Penn State U.) , Gianluca Calcagni, (Potsdam, Max Planck Inst.) , Shinji Tsujikawa, (Tokyo U. of Sci.) . AEI-2011-042, Jul 2011. 37pp.
Published in JCAP 1111:046,2011.
e-Print: arXiv:1107.1540 [gr-qc] (15)

15) Non-singular inflationary universe from polymer matter.
Golam Mortuza Hossain, Viqar Husain, Sanjeev S. Seahra, (New Brunswick U.) . Jun 2009. (Published Jan 15, 2010). 4pp.
Published in Phys.Rev.D81:024005,2010.
e-Print: arXiv:0906.2798 [astro-ph.CO] (13)

16) Constraints on standard and non-standard early Universe models from CMB B-mode polarization.
Yin-Zhe Ma, (Cambridge U., KICC & Cambridge U., Inst. of Astron.) , Wen Zhao, (Cardiff U.) , Michael L. Brown, (Cambridge U., KICC & Cambridge U., Inst. of Astron. & Cambridge U.) . Jul 2010. 41pp.
Published in JCAP 1010:007,2010.
e-Print: arXiv:1007.2396 [astro-ph.CO] (11)

17) Loop Quantum Cosmology corrections on gravity waves produced during primordial inflation.
J. Grain, (Paris, Inst. Astrophys.) . Nov 2009. 9pp.
To appear in the proceedings of INVISIBLE UNIVERSE INTERNATIONAL CONFERENCE: Toward a new cosmological paradigm, Paris, France, 29 Jun - 3 Jul 2009.
Published in AIP Conf.Proc.1241:600-608,2010.
e-Print: arXiv:0911.1625 [gr-qc] (9)

18) Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background: Phenomenology and Fundamental LQC Parameters.
Julien Grain, (Paris, Inst. Astrophys. & Orsay, LAL) , Aurelien Barrau, Thomas Cailleteau, (LPSC, Grenoble) , Jakub Mielczarek, (Jagiellonian U.) . Nov 2010. (Published Dec 15, 2010). 12pp.
Published in Phys.Rev.D82:123520,2010.
e-Print: arXiv:1011.1811 [astro-ph.CO] (9)

19) Warm inflationary model in loop quantum cosmology.
Ramon Herrera, (Rio de Janeiro, Pont. U. Catol.) . Jun 2010. (Published Jun 15, 2010). 15pp.
Published in Phys.Rev.D81:123511,2010.
e-Print: arXiv:1006.1299 [astro-ph.CO] (8)

20) The Big Bang and the Quantum.
Abhay Ashtekar, (Penn State U.) . May 2010. 18pp.
Plenary talk at INVISIBLE UNIVERSE INTERNATIONAL CONFERENCE: Toward a new cosmological paradigm, Paris, France, 29 Jun - 3 Jul 2009.
Published in AIP Conf.Proc.1241:109-121,2010.
e-Print: arXiv:1005.5491 [gr-qc] (7)

21) On the measure problem in slow roll inflation and loop quantum cosmology.
Alejandro Corichi, (UNAM, Morelia, Inst. Math. & Penn State U.) , Asieh Karami, (IFM-UMSNH, Michoacan & UNAM, Morelia, Inst. Math.) . Nov 2010. (Published May 15, 2011). 12pp.
Published in Phys.Rev.D83:104006,2011.
e-Print: arXiv:1011.4249 [gr-qc] (7)

 

[marcus]

Besides cosmology (eg Higgs inflation in Loop cosmo) the other 6 topics to watch, that I listed in post #87 and don't want to completely forget about, are as follows:

Stacking refers to Lewandowski group's way to systematically ENUMERATE and compute spinfoam histories. They stack up successive spin network states of geometry and join them into a single history.
http://arxiv.org/abs/1107.5185

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

Unclamping the Immirzi parameter was a consequence of Bianchi's black hole entropy result S=A/4. It appears to me to have exciting and unpredictable implications for the theory.
http://arxiv.org/abs/1204.5122

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

Thermodynamics of geometry is the theme of some recent papers by Jacobson, Smolin, Padmanabhan and others. Could the Einstein GR equation be (like PV = NkT) the equation of state describing overall behavior of microscopic variables (like the vast number of gas molecules whose collective behavior is summarized by PV = NkT.) If GR is the equation of state, what are the underlying degrees of freedom? Do spinfoams describe the underlying degrees of freedom for which EFE is the EoS?
http://arxiv.org/abs/1204.6349 http://arxiv.org/abs/1205.5529 http://arxiv.org/abs/1207.0505

Dust is shorthand for the various approaches being used to recover a real physical Hamiltonian. Members of both the Erlangen and Warsaw groups have research along several related lines. This is familiar from cosmology and I think it's of considerable practical value.
http://arxiv.org/abs/1206.3807 http://arxiv.org/abs/1206.0658

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

Actually something just came out today that relates to the "Tetrad sign" idea:

http://arxiv.org/abs/1207.5156
Divergences and Orientation in Spinfoams
Marios Christodoulou, Miklos Långvik, Aldo Riello, Christian Röken, Carlo Rovelli
(Submitted on 21 Jul 2012)
We suggest that large radiative corrections appearing in the spinfoam framework might be tied to the implicit sum over orientations. Specifically, we show that in a suitably simplified context the characteristic "spike" divergence of the Ponzano-Regge model disappears when restricting the theory to just one of the two orientations appearing in the asymptotic limit of the vertex amplitude.
10 pages, 5 figures

For example reference [13] is to the original tetrad sign paper by Rovelli&Wilson-Ewing which enters discussion on page 1 here:

==quote page 1 of Christodoulou et al==
We suggest here that the answer lies in the fact that the asymptotic limit of the Ponzano-Regge amplitude is not the exponential of the Regge action, but rather the sum of two exponentials of the Regge action, taken with certain flipped signs. With flipped signs, the invariant contribution comes when P is outside τ. In other words, the divergence is strictly dependent on the existence of the second term in the expansion of the vertex amplitude.

The geometrical origin of this second term can be traced to the fact that the asymptotic limit of the Ponzano-Regge model is not truly 3d general relativity in metric variables, but rather 3d general relativity in triad variables, with an action that flips sign under reversal of the orientation of the triad [13]. In three dimensions, it is this action (and not metric general relativity) which is equivalent to BF theory. In turn, BF theory has an additional gauge symmetry with respect to general relativity: the shift B → B+d_AΦ (where A is the connection variable: F = dA+A∧A), which can be shown to be related to the displacement of P all over the hyperplane [4].

In this paper, we present two arguments that provide some ground for these intuitions...
==endquote==

 

[marcus]

So as not to forget the active lines of research we're following:
PhenoCosmo (bounce early universe cosmology is where pheno enters most strongly)
Stacking
Histories
Unclamping
Tetrad-handedness
Thermo
Dust

I see that someone named David Craig has some potentially Loop-related consistent/decoherent "Histories" papers.
http://arxiv.org/find/gr-qc/1/au:+Craig_D/0/1/0/all/0/1
Somehow I was not aware of his research until now.
He has co-authored two papers with Loop researcher Param Singh, and also co-authored with Jim Hartle, Fay Dowker, Rafael Sorkin. Recently brought out his first explicitly Loop cosmology paper.

To keep track of a few of the authors involved in each of these research lines, for reference purposes:
PhenoCosmo (Barrau, Grain, Pawlowski, Cailleteau, Agullo, Nelson, Vidotto,...)
Stacking (Lew., ... )
Histories (Hartle, Schroeren?, Craig?)
Unclamping (Bianchi, ...)
Tetrad-handedness (Rov., ...)
Thermo (Jac., Smo., Pad., ...)
Dust (Lew., Thiem., Wise, ...)

 

[marcus]

I forgot TWISTORS when listing active lines of Loop research which could feature in whatever reformulation takes shape at the July 2013 Perimeter conference. This just came out:
http://arxiv.org/abs/1207.6348
The twistorial structure of loop-gravity transition amplitudes
Simone Speziale, Wolfgang M. Wieland
(Submitted on 26 Jul 2012)
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial description, which brings new light on both classical and quantum aspects of the theory. At the classical level, we clarify the covariant properties of the discrete geometries involved, and the role of the simplicity constraints in leading to SU(2) Ashtekar-Barbero variables. We identify areas and Lorentzian dihedral angles in twistor space, and show that they form a canonical pair. The primary simplicity constraints are solved by simple twistors, parametrized by SU(2) spinors and the dihedral angles. We construct an SU(2) holonomy and prove it to correspond to the Ashtekar-Barbero connection. We argue that the role of secondary constraints is to provide a non trivial embedding of the cotangent bundle of SU(2) in the space of simple twistors. At the quantum level, a Schroedinger representation leads to a spinorial version of simple projected spin networks, where the argument of the wave functions is a spinor instead of a group element. We rewrite the Liouville measure on the cotangent bundle of SL(2,C) as an integral in twistor space. Using these tools, we show that the Engle-Pereira-Rovelli-Livine transition amplitudes can be derived from a path integral in twistor space. We construct a curvature tensor, show that it carries torsion off-shell, and that its Riemann part is of Petrov type D. Finally, we make contact between the semiclassical asymptotic behaviour of the model and our construction, clarifying the relation of the Regge geometries with the original phase space.
39 pages

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

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

 

[marcus]

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

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

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

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

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

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

 

[marcus]

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

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

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

FreeImmirzi was a consequence of Bianchi and others' black hole entropy result S=A/4. It appears to have exciting and unpredictable implications for the theory.
http://arxiv.org/abs/1204.5122

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

Stacking refers to Lewandowski group's way to systematically ENUMERATE and compute spinfoam histories. They stack up successive spin network states of geometry and join them into a single history.
http://arxiv.org/abs/1107.5185

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

Thermodynamics of geometry is the theme of some recent papers by Jacobson, Smolin, Padmanabhan and others. Could the Einstein GR equation be (like PV = NkT) the equation of state describing overall behavior of microscopic variables (like the vast number of gas molecules whose collective behavior is summarized by PV = NkT.) If GR is the equation of state, what are the underlying degrees of freedom? Do spinfoams describe the underlying degrees of freedom for which EFE is the EoS?
http://arxiv.org/abs/1204.6349 http://arxiv.org/abs/1205.5529 http://arxiv.org/abs/1207.0505

Dust is shorthand for the various approaches being used to recover a real physical Hamiltonian. Members of both the Erlangen and Warsaw groups have research along several related lines. This is familiar from cosmology and I think it's of considerable practical value.
http://arxiv.org/abs/1206.3807 http://arxiv.org/abs/1206.0658

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

 

[marcus]

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

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

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

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

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

 

[marcus]

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

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

http://www-library.desy.de/cgi-bin/spifaacce/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29

Here's a revised listing with some PhenoCosmo sample links:
PhenoCosmo Observable effects of the Loop cosmology bounce and of bounce-triggered inflation.
Ashtekar, Agullo, Nelson http://arxiv.org/abs/1204.1288 (Perturbations in loop quantum cosmology)
Artymowski, Dapor, Pawlowski http://arxiv.org/abs/1207.4353 (Inflation from non-minimally coupled scalar field in loop quantum cosmology)
By various of the following: Barrau, Grain, Cailleteau, Vidotto, Mielczarek
http://arxiv.org/abs/1206.6736 (Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology)
http://arxiv.org/abs/1206.1511 (Loop quantum cosmology in the cosmic microwave background)
http://arxiv.org/abs/1111.3535 (Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology)
http://arxiv.org/abs/1011.1811 (Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background: Phenomenology and Fundamental LQC Parameters)
http://arxiv.org/abs/1003.4660 (Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves)

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

FreeImmirzi was a consequence of Bianchi and others' black hole entropy result S=A/4. It appears to have exciting and unpredictable implications for the theory.
http://arxiv.org/abs/1204.5122

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

Stacking refers to Lewandowski group's way to systematically ENUMERATE and compute spinfoam histories. They stack up successive spin network states of geometry and join them into a single history.
http://arxiv.org/abs/1107.5185

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

Thermodynamics of geometry is the theme of some recent papers by Jacobson, Smolin, Padmanabhan and others. Could the Einstein GR equation be (like PV = NkT) the equation of state describing overall behavior of microscopic variables (like the vast number of gas molecules whose collective behavior is summarized by PV = NkT.) If GR is the equation of state, what are the underlying degrees of freedom? Do spinfoams describe the underlying degrees of freedom for which EFE is the EoS?
http://arxiv.org/abs/1204.6349 http://arxiv.org/abs/1205.5529 http://arxiv.org/abs/1207.0505

Dust is shorthand for the various approaches being used to recover a real physical Hamiltonian. Members of both the Erlangen and Warsaw groups have research along several related lines. This is familiar from cosmology and I think it's of considerable practical value.
http://arxiv.org/abs/1206.3807 http://arxiv.org/abs/1206.0658

 

[marcus]

One of the categories in the preceding post needs enlargement.

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

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

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

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

 

[marcus]

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

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

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

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

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

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

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

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

 

[marcus]

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

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

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

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

 

[marcus]

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

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

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

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

Invited Speakers (Titles and Abstracts)

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

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

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

 

[atyy]

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

No more spin networks - just spin nets

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

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

 

[marcus]

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

I have highlighted the abstracts of Alesci, Bahr, Ding, Wieland, and Zhang as a reminder of topics to look into further.

 

[atyy]

It looks to me as if the way she uses "spin nets" they are not DUAL to spinfoam but rather, as she says, a dimensional reduction of spinfoams. Dittrich's pattern seems to be to explore variants, toy models, simplified (often lower dimensional) versions, to get a better understanding of the mathematics.

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

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

I believe Dittrich and Gu and Wen are talking about related things, because both refer to Levin and Nave as the basis for tensor network renormalization. Ah, yes, they are the same thing, she cites Levin and Nave and Gu and Wen on slide 21 of http://www.ucm.es/info/giccucm/Escorial2011/Dittrich.pdf .

 

[marcus]

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

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

 

[marcus]

Incidentally at the science level, the organizers of Loops 2013 are Dittrich, Freidel, Smolin. It will be enlightening to see how they sort out the topics and evalutate directions in current Loop research, as they construct the program and arrange the plenary talks and parallel sessions.
http://www.perimeterinstitute.ca/en/Events/Loops_13/Loops_13/
Also I would suggest anyone who hasn't seen it check out Dittrich Freidel Smolin's listing of their International Advisory Committee at the Loops 13 webpage.
Since I haven't done this in a while, I'll update the list of potential reformulation topics I'm watching.

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

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

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

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

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

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

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

Dust is shorthand for the various approaches being used to recover a real physical Hamiltonian. Members of both the Erlangen and Warsaw groups have research along several related lines. This is familiar from cosmology and I think it's of considerable practical value.
http://arxiv.org/abs/1206.3807 http://arxiv.org/abs/1206.0658

 

[marcus]

In the preceding I listed 8 frontier categories, look back to see definitions and links to sample research. The third was too narrow and should be made to include Tensorial GFT. I have enlarged it here and tentatively call it Algebraic generalizations. Here is the revised stripped down list.

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

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

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

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

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

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

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

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

Progress occurring on some or all of these fronts could be expected to show up in the program at Loops 2013:
http://www.perimeterinstitute.ca/en/Events/Loops_13/Loops_13/
or possibly earlier at the GR20 meeting in Warsaw.
http://gr20-amaldi10.edu.pl