Expectations for LQG in 2009: New Developments and Connections to LQC

[marcus]

I'll risk some projections, so if I'm wrong if anyone wants they can fish up this thread 10 months down the road and say "hah hah it didn't happen".

Anyway it can help to have an idea of what changes to expect----some rough idea of the recent past and the near future. So here' what I think will happen in LQG in 2009.

In 2007 we got a new LQG which is Lorentz covariant and as Rovelli says amounts to a rederivation of the old canonical LQG.
Significant results and features carry over, enough so that it looks to me as if one can pretty much discard old LQG if one wants. For some years the more significant research has been in the area of spinfoam and group field theory. Now there's a new LQG vertex that reproduces all that matters from the old version.

The new LQG is manifestly background independent in the sense that LQG people use this term. It's formulation does not require assuming any background spacetime metric. In fact it is not clear to me that it even requires assuming much if anything about spacetime topology. You seem able to set up the theory without any background continuum at all. A spinfoam is a relational structure defined in a purely combinatorial way. That's my view, maybe someone who knows better will want to correct me on this.

There is an obvious way to add matter fields (to spin networks and spinfoam) which has always been known. The matter fields live on the state of geometry, e.g. the network, and do not need to be defined on a continuum. The best introductory overview talk I know is Rovelli's invited presentation to the Strings 2008 conference. Here's the video and the slides.

http://cdsweb.cern.ch/record/1121957?ln=en
http://indico.cern.ch/getFile.py/access?contribId=30&resId=0&materialId=slides&confId=21917

At this point most of the research effort is focused on showing that the low-energy limit of the new LQG is right. There've been a lot of papers on this advancing piece by piece and case by case. Here's my expectation:

They will have a substantial chunk of that done by September.

The next major agenda item is testability, and to achieve that they need to connect LQG and LQC. That's actually the main thing I'm interested in watching this year. I think the low energy limit is a done deal. So I'm especially on the look-out for papers that bridge the gap between LQG and LQC.

Here's a fore-runner of the effort to do that---a paper by Jon Engle. My expectation is there will be a bunch more papers this year along this line.
Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings.
Jonathan Engle (Marseille, CPT & Provence U. & Marseille U., Luminy) . 20pp.
Published in Class.Quant.Grav.24:5777-5802,2007.
e-Print: gr-qc/0701132

 

[marcus]

The gap between LQG and LQC is, in my view, primarily formal. So far it is impossible to mathematically derive one from the other. The aim of LQC is to do a simplified version of LQG under the uniformity assumptions of cosmology: the homogeneous and isotropic universe.

So I expect a radical increase in the effort devoted to relaxing those simplifying assumptions---extending LQC to cases where isotropy, for instance, is broken. Cases where the state of the universe is not the same in all directions. Or where the requirement of homogeneity is relaxed.

Rovelli is already on board with that effort:
http://arxiv.org/abs/0805.4585
Stepping out of Homogeneity in Loop Quantum Cosmology
Carlo Rovelli, Francesca Vidotto
16 pages
(Submitted on 29 May 2008)
"We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable effective dynamics within this approximation."

This is another sign-post of what to expect.

Oh, the reason it's vital to bridge LQG and LQC is obviously testability. This earlier thread was about that:
https://www.physicsforums.com/showthread.php?t=294456
That thread cited a number of papers indicating that it is reasonable to suppose that LQC is testable by practical instruments some of which are already being made ready. Opinions can obviously differ on this until it actually happens. The general idea is that cosmology compensates in various ways for the extremity of Planck scale and makes physics at that level more approachable.

 

[ensabah6]

In 2007 we got a new LQG which is Lorentz covariant and as Rovelli says amounts to a rederivation of the old canonical LQG.

At this point most of the research effort is focused on showing that the low-energy limit of the new LQG is right. There've been a lot of papers on this advancing piece by piece and case by case. Here's my expectation:

They will have that done by September. e-Print: gr-qc/0701132

What is this "new" LQG -- and what papers are chipping away at its low energy limit is GR? Is it Eyo Ita or something else you have in mind?

 

[marcus]

Some folks may not have been paying attention to the changes going on in LQG and need some way to catch up.
I've got some links and lists of the most highly cited recent (2007 and later) papers in a thread called Introduction to LQG. Only the most recent posts are relevant.
https://www.physicsforums.com/showthread.php?p=2096329#post2096329
If you do a search for LQG papers (2007 and later) ranked by citation, the almost the entire top twenty will be new LQG, or else new LQC (a new version of LQC came in around 2006-2007 too).

There is another thread called Covariant LQG and its low energy limit, that discusses the change in LQG.
https://www.physicsforums.com/showthread.php?t=292384
If you have questions about the work going on to establish the low energy limit, please read the relevant links in that thread and if you have questions feel free to post them there.

 

[ensabah6]

thanks.

So if I were to summarize your point in a nutshell:

Rovelli has worked on a new spinfoam model 4D with Imirizi parameter that avoids the pitfalls of the older Barret-Crane SF models, which makes contact with canonical LQG kinematics, and that by Sept, you think he'll publish papers which show that these new SF models will have good semiclassical limit, perhaps a first.

 

[marcus]

Rovelli summed up the situation as he saw it as of 30 December 2008 in their latest paper:

==quote==
4 Conclusions
What we have shown here is only that the obstacle that prevented the Barrett-Crane vertex to yield the proper graviton propagator is resolved by the new vertex. Clearly it is now necessary to restart from scratch the calculation of the graviton propagator using the new vertex, and check that everything works properly.
... The full calculation of the graviton two-point function using the Livine-Speziale basis is in course, and will be presented elsewhere. Calculations of higher-n, n-point functions and higher-order terms of the propagator are also in course.
A number of issues need better clarification before we can say that we understand the low energy limit of loop quantum gravity. Among these the role of gauge invariance [26] and finiteness [27]. Nevertheless, we see good reasons for optimism. The new vertex has been introduced in [7, 10] only as an attempt to give the intertwiners a dynamics. Whether this dynamics was correct at low-energy remained unclear during the last year, lacking the asymptotic analysis of the vertex. Remarkably, this analysis turns out to give precisely the intertwiner dependence that was previously indicated as the one hoped for.
==endquote==

I would say it is reasonable to expect at a minimum the graviton two-point function to be calculated by September, but actually I expect considerably more to have happened by then. And I don't expect the papers appearing between now and then to be all by Rovelli . There are half a dozen or more other people at the forefront of this as well (Engle, Dittrich, Speziale, Pereira, Alesci, Bianchi,...) not to mention better-known names like Barrett, Freidel and Livine.

The paper I quoted here is the third in a landmark series:
http://arxiv.org/abs/0812.5018
LQG propagator: III. The new vertex
Emanuele Alesci, Eugenio Bianchi, Carlo Rovelli
9 pages
(Submitted on 30 Dec 2008)
"In the first article of this series, we pointed out a difficulty in the attempt to derive the low-energy behavior of the graviton two-point function, from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that this difficulty disappears when using the corrected vertex amplitude recently introduced in the literature. In particular, we show that the asymptotic analysis of the new vertex amplitude recently performed by Barrett, Fairbairn and others, implies that the vertex has precisely the asymptotic structure that, in the second article of this series, was indicated as the key necessary condition for overcoming the difficulty."

My guess is that anyone serious about following LQG read this paper when it came out and formed their own impressions. I've also recommended watching one recent Perimeter talk video, namely that of Roberto Pereira. I've given the link elsewhere but in case anyone is interested and missed it, here it is again. If you have trouble getting the audio in synch please let me know.
http://pirsa.org/08120046/
Loop quantum gravity vertex for spin foam gravity
Roberto Pereira - CPT Marseille
"New spin foam models for gravity have been recently proposed to deal with the shortcomings of the Barrett-Crane model. In particular, they draw a closer connection between the Loop Quantum Gravity and the Spin Foam approaches to non perturbative quantum gravity. In this talk, I will present the construction for the case of Lorentzian signature and finite Immirzi parameter. An area operator can be defined and its spectrum agrees with the one defined in LQG. Finally, the amplitude is shown to be finite after a suitable regularization."

Two earlier papers by Pereira
http://arxiv.org/abs/0710.5043
Lorentzian LQG vertex amplitude
http://arxiv.org/abs/0805.4696 (with Jon Engle)
Regularization and finiteness of the Lorentzian LQG vertices

Watching the video of Pereira's talk gave me a new respect for the group of people Rovelli has brought into this research. As a seminar talk it is more forward looking to new developments compared with a journal article which is necessarily more after the fact, and backward looking. In a seminar talk you discuss with immediate colleagues what you are doing now. So it can be a better predictor. I would suggest that anyone seriously paying attention to LQG developments watch the video. Let me know if you have trouble with audio synch.

 

[ensabah6]

Interesting, thanks. He raises other issues including finiteness but doesn't state whether new Rovelli SF models (or even old sf models) ability to reproduce flat spacetime coupled to SM QFT as part of the low energy limit?

 

[marcus]

I should update this thread.
The three areas where I think we should be looking for progress this year are
1. the low energy limit
2. connecting LQC with LQG
3. testability (e.g. work involving black holes, GRBs, observable features of the early universe)

What has happened already in 2009 that has a bearing on these three goals?

1. So far progress towards understanding the LQG low energy limit is best described in the abstract Rovelli gave for his planned series of talks in October. I also found Claudio Perini's February 2009 Perimeter Seminar (PIRSA) talk contained a useful perspective on the latest spinfoam work.
See http://www.maths.nottingham.ac.uk/qg/CorfuSS.html or simply google "Corfu QG school"
For Perini's PIRSA talk, just google "perini pirsa". It should come up.
Or go here:
http://pirsa.org/09020023/

2. Today's ILQGS talk by Adam Henderson gave some indication of where things are going with the effort to bridge LQG with LQC. The talk was on a path integral form of LQC (which would bring the quantum cosmology application closer to the main theory). It was interspersed with much discussion by people like Krasnov (Nottingham), Freidel (Perimeter) and Ashtekar (Henderson's advisor at Penn State).
http://relativity.phys.lsu.edu/ilqgs/ or google "ILQGS" for international lqg seminar.

3. Testability is probably the most distant goal. The topic list for the August 2009 Beijing Loops conference can be read as an agenda for approaching it.
* Loop quantum gravity
* Loop quantum cosmology and other symmetric models
* Spin foams and their low energy ramifications
* Fundamental questions of quantum gravity
* Black holes and Cosmology related to quantum gravity
* Phenomenology of quantum gravity

Simply google "Loops 09 Beijing" or go to
http://www.loops09.org/index.htm and
http://www.loops09.org/School/School-en.htm

The first three topics have to do with linking together canonical LQG, and the spinfoam covariant version, with Loop Cosmology.
And also (referring to topic 3) determining the low energy limit

The last two topics, which I highlighted, have to do with prediction and observation. Black holes, Gammaray Bursts, and Early Universe phenomena are places where one can hope that Planck scale physics may be revealed and LQG predictions tested.

My previous remark about Perimeter seminar talks by recent Marseille PhDs applies in spades to the one by Perini. It's worth watching. The title is
Graviton propagator from EPRL spinfoam model
As I said, to get it all you need to do is google "perini pirsa"

 

[ensabah6]

you obviously know this paper

http://arxiv.org/abs/0903.4329
Graviton propagator as a tool to test spinfoam models
Emanuele Alesci

I thought spinfoams were distinct from LQG in Ashketar variables, as there is no proof a Feynman Kac like formula between the Hamiltonian and spinfoam, and that if SF does have the correct semiclassical limit, there are still ambiguities in the hamiltonian formulation.

 

[marcus]

Things continue to proceed somewhat as expected. About the low energy or semiclassical limit of LQG (by which I mean the spinfoam version) we now have the abstract of Laurent Freidel's invited plenary talk to the 13 July Marcel Grossmann meeting in Paris ("MG12")
http://www.icra.it/MG/mg12/en/invited_speakers_details.htm#freidel

Laurent Freidel
Talk: Spin Foam models: models of quantum dynamical space time

Abstract: In this talk I will give an overview of spin foam models which describe the dynamics of quantum gravity in a background independent context. I will focus especially on the recent developments which concern the construction of these models in 4 dimensional gravity and present some of the key results obtained in this context like the construction of the model, the proof of the semi-classical limit and the relationship with loop quantum gravity and SU(2) spin network states.

I already quoted the abstract of Carlo Rovelli's series of lectures to be given at the Corfu QG school in September.
See http://www.maths.nottingham.ac.uk/qg/CorfuSS.html or simply google "Corfu QG school"

...
The three areas where I think we should be looking for progress this year are
1. the low energy limit
2. connecting LQC with LQG
3. testability (e.g. work involving black holes, GRBs, observable features of the early universe)...

Also about verifying the correct limits of spinfoam LQG, there was Perini's PIRSA talk that I mentioned earlier. Just google "perini pirsa" or go here:
http://pirsa.org/09020023/
Graviton propagator from EPRL spinfoam model
I learned recently that the paper will appear soon that this talk was based on. It is by Claudio Perini, Elena Magliari, Eugenio Bianchi.

About the effort to bridge LQG with LQC, there are actually many papers that have been appearing. I mentioned one result that seemed especially significant, the LQC path integral. See Adam Henderson's ILQGS talk (audio and pdf online):
http://relativity.phys.lsu.edu/ilqgs/ or google "ILQGS" for international lqg seminar.

 

[marcus]

One of the Pf posters just wrote to ask about current status and progress of LQG and reminded me that in this earlier thread I hazarded some personal guesses about how things would go this year.
What I said was:

...
The three areas where I think we should be looking for progress this year are
1. the low energy limit
2. connecting LQC with LQG
3. testability (e.g. work involving black holes, GRBs, observable features of the early universe)...​

So let's summarize and update this thread and see how things are going (partly in response to that other poster.)

Currently the best overview is Rovelli's Strings 2008 talk (online CERN video).

Going forward, the best overview will be Rovelli's September 2009 Corfu lectures.

The deepest insight into what LQG and the halfdozen other backgroundless quantum geometry/gravity approaches are really about. And how they are indistinguishable different versions of each other, at a certain level. How someone who does Lqg should be thinking about Lqg. that would be a 20 minute segment in the middle of a "Trialogue" Seminar by Ashtekar-Rovelli-Freidel in the ILQGS (int'l lqg seminar) series.

For a LQG exposition/survey paper, the Albert Einstein Institute has Living Reviews on line and Rovelli just updated his review of Lqg there in spring of 2008.

All this stuff can be easily googled. The most timely, which I will paste in here, is the abstract for the Corfu lectures.
The context is:
http://www.maths.nottingham.ac.uk/qg/CorfuSS.html

Each of the main speakers will give a series of lectures during the course of the week (a minicourse):

Abhay Ashtekar Loop Quantum Gravity

John Baez Categorification in Fundamental Physics

John Barrett Spin networks and quantum gravity

Vincent Rivasseau Renormalization in Fundamental Physics

Carlo Rovelli Covariant loop quantum gravity and its low-energy limit

Here is Rovelli's description of his series of lectures:

"I present a new look on Loop Quantum Gravity, aimed at giving a better grasp on its dynamics and its low-energy limit. Following the highly successful model of QCD, general relativity is quantized by discretizing it on a finite lattice, quantizing, and then studying the continuous limit of expectation values. The quantization can be completed, and two remarkable theorems follow.

The first gives the equivalence with the kinematics of canonical Loop Quantum Gravity.
This amounts to an independent re-derivation of all well known Loop Quantum gravity kinematical results.

The second [gives] the equivalence of the theory with the Feynman expansion of an auxiliary field theory. Observable quantities in the discretized theory can be identified with general relativity n-point functions in appropriate regimes. The continuous limit turns out to be subtly different from that of QCD, for reasons that can be traced to the general covariance of the theory.

I discuss this limit, the scaling properties of the theory, and I pose the problem of a renormalization group analysis of its large distance behavior."

About the second agenda item on that list, connecting LQC with LQG, we should probably not lose track of Henderson's ILQGS talk in March of this year:
https://www.physicsforums.com/showthread.php?t=300439
This gives (for the first time) a path integral formulation of LQC. This makes it more immediately compatible with the way the main LQG theory is being handled.