Reformulation of Loop gravity in progress, comment?

[marcus]

Although not well enough informed to give a professional level "progress report" for Loop research, in view of Tom's question I'll give some opinions and impressions. The following two papers tend to EMBED Loop cosmology in the full theory, thus making the full theory astrophysically testable.
I think these two represent some of the most important recent progress.

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

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

The most important progress any QG theory can make is progress towards testability and this can be of two kinds, IMHO:
1) Observable consequences in early universe astrophysics.
2) LHC-testable consequences of unification of gravity with particle physics.

As to point 1), there has been substantial progress towards deriving observable consequences of Loop cosmology--more than I can readily list or outline. Here is a recent example. See also papers by Barrau, Grain, and co-authors.

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

Here are the quantum cosmology papers that the INSPIRE search engine identifies (appeared since 2009, ranked by cite count.) This includes Loop AND all the other kinds of quantum cosmology. So one can compare and get a sense of the relative importance.
http://inspirehep.net/search?ln=en&...2y=2013&sf=&so=a&rm=citation&rg=50&sc=0&of=hb

As to point 2) there has, to my knowledge, been slight progress thus far. A beginning was made last year in the work of Alexander, Marciano, and Smolin. We'll have to see how that goes.

I suspect that any "progress report" for Loop should mention Wieland's recent paper. It addresses many issues---joining the Hamiltonian and Spinfoam approaches---understanding the various conditions and constraints. Basically learning how to put the theory in a nice form. Again we will have to see how this work continues.
http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

In one point I find I can't cover all the topics! Just in the past year there has also been remarkable progress in studying the Loop black hole.

I will have to redo this and try to organize it better.

 

[tom.stoer]

Marcus, my question was about LQG as the general framework, not about LQC.

 

[marcus]

Marcus, my question was about LQG as the general framework, not about LQC.

I know. I don't think that is the best way to look at it.
I explained why in post #149

QC is the overall framework for quantum gravity.
It contains the big thing we want to understand.
It has a huge amount of relevant data.
It is the arena of testability.

So QC is the natural framework to consider.

 

[tom.stoer]

Marcus, I disagree. QG is the basis, QC is an application.

Cosmology is an application of GR which provides the fundamental framework - not the other way round.

 

[marcus]

Progress in QG can only be understood in the larger QC context.
Cosmology is what gives scientific meaning and urgency to the study of geometry at Planck scale.

Cosmology is what gives us the questions:
dark matter
expansion of distances between stationary observers
the fact that geometry is dynamic
the fact that there is another gravitational constant Lambda which Newton didn't know about
how does matter behave in extreme dynamic geometry?
etc.

And Cosmology is where the great bulk of observational data is, that is relevant
to quantum gravity.

So to me it seems inevitable to conclude that QC provides the larger context in which LQG progress
must be assessed. If one is to make a meaningful assessment, that is.

 

[tom.stoer]

Cosmology is relevant as one application and as 'experimental setup'. But the develoment of a theory like QG focusses on a sound mathematical construction, of course to be tested in a larger context.

The development of GR was focussed on symmetry principles, field equations etc., not on expanding universes. The construction of QM was focussed on matrix and wave mechanics, not on spectroscopy.

Of course you have to apply a theory in larger context, and you have to have quantitative predictions and means to falsify the model. But first you have to have a model (or a class of models) passing basic tests like mathematical consistency, absence of anomalies, GR as semiclassical limit, ...

Looking at the current status of LQG most astrophysical data do not help much. They have to get the math right (and the latest spinor/twistor papers indicate that the celebrated Rovellian models are still incomplete). Assume we have a new deep space survey providing revolutionary results regarding CMB, galaxy superclusters or even the topology of our universe. This wouldn't change the status of LQG, unfortunately. They are not (yet) in the situation to select from a class of well-defined models based on experimental input. They are still in the construction phase.

 

[marcus]

Cosmology is relevant as one application and as 'experimental setup'. But the develoment of a theory like QG focusses on a sound mathematical construction, of course to be tested in a larger context.

The development of GR was focussed on symmetry principles, field equations etc., not on expanding universes. The construction of QM was focussed on matrix and wave mechanics, not on spectroscopy.

Of course you have to apply a theory in larger context, and you have to have quantitative predictions and means to falsify the model. But first you have to have a model (or a class of models) passing basic tests like mathematical consistency, absence of anomalies, GR as semiclassical limit, ...

Looking at the current status of LQG most astrophysical data do not help much. They have to get the math right (and the latest spinor/twistor papers indicate that the celebrated Rovellian models are still incomplete). Assume we have a new deep space survey providing revolutionary results regarding CMB, galaxy superclusters or even the topology of our universe. This wouldn't change the status of LQG, unfortunately. They are not (yet) in the situation to select from a class of well-defined models based on experimental input. They are still in the construction phase.

You have some good points here. Let me try to say my idea in a different way. LQG is thought of as a pure gravity program---the quantum dynamics of pure matterless geometry.
I watch the research closely (as closely as I, as non-expert, can) and I see a trend. You could think of it as the emergence of a new field of research called LQGM ("loop quantum geometry-and-matter").

I can try to make a general statement about this. Let's see if this is right: LQGM arises from the application of principles of loop quantum gravity (LQG) to general relativity and standard matter theory. The goal is to quantize Plebanskian action containing GR and the local symmetries of standard matter, by following the physical ideas and mathematical tools underlying LQG.

Basically this involves building a more general theory, of which some version of the old LQG might turn out to be a special case. The important thing is that the new theoretical program follows the physical ideas and applies the mathematical tools developed in the more specialized earlier program.

Does this make sense to you? Many of the leading people I can think of who used to be working on the more limited specialized LQG program I now see to be working on combining geometry with matter in one way or another---creating, in effect, a broader more general program (undoubtably with some new mathematical tools and possibly with some new principles besides those developed in the earlier program.)

If you would like, I will try to enumerate the people involved in this move, and some of the papers. Let me know what you think, and what (if any) additional information you require.

 

[tom.stoer]

I can't see this big move and I think that incorporating matter has something to do with the key issues like definition of Dirac-observables, physical observers, gauge fixing/unfixing etc. And I think it's a new line of research, but not a paradigm shift.

But besides these details, responding to your question whether it makes sense to me: yes, it does.

 

[marcus]

I can't see this big move and I think that incorporating matter has something to do with the key issues like definition of Dirac-observables, physical observers, gauge fixing/unfixing etc. And I think it's a new line of research, but not a paradigm shift.

But besides these details, responding to your question whether it makes sense to me: yes, it does.

Your question about progress of the purely QG part of the program also makes sense to me, although I take a broader view of the program. On the SPINORIAL formulation front, Etera Livine offers this as a review.
http://arxiv.org/abs/1201.2120
It's a paper by Dupuis Speziale Tambornino called
Spinors and Twistors in Loop Gravity and Spin Foams
"Spinorial tools have recently come back to fashion in loop gravity and spin foams. They provide an elegant tool relating the standard holonomy-flux algebra to the twisted geometry picture of the classical phase space on a fixed graph, and to twistors. In these lectures we provide a brief and technical introduction to the formalism and some of its applications."

Here's a recent paper by Livine himself:
http://arxiv.org/abs/1302.7142
Holonomy Operator and Quantization Ambiguities on Spinor Space
Etera R. Livine
(Submitted on 28 Feb 2013)
"We construct the holonomy-flux operator algebra in the recently developed spinor formulation of loop gravity. We show that, when restricting to SU(2)-gauge invariant operators, the familiar grasping and Wilson loop operators are written as composite operators built from the gauge-invariant 'generalized ladder operators' recently introduced in the U(N) approach to intertwiners and spin networks. We comment on quantization ambiguities that appear in the definition of the holonomy operator and use these ambiguities as a toy model to test a class of quantization ambiguities which is present in the standard regularization and definition of the Hamiltonian constraint operator in loop quantum gravity."

Livine is to be one of the invited speakers at Loops 2013 and my guess is he will summarize what is going on in this area. At this point I can't do better than simply refer to what he indicates is the review paper of choice (Dupuis, Speziale, Tambornino).

 

[marcus]

The earlier interesting discussion with Tom helped me to clarify my view that the hallmark of any QG theory is how it deals with cosmology (and the start of expansion in particular.)
The robust identifying feature of Loop Quantum Geometry has been that it leads back to a bounce with a period of natural faster-than-exponential expansion ("superinflation") due to quantum effects at high density. To summarize:

Progress in QG can only be understood in the larger QC context.
Cosmology is what gives scientific meaning and urgency to the study of geometry at Planck scale.

Cosmology is what gives us the questions:
dark matter
expansion of distances between stationary observers
the fact that geometry is dynamic
the fact that there is another gravitational constant Lambda which Newton didn't know about
how does matter behave in extreme dynamic geometry?
etc.

And Cosmology is where the great bulk of observational data is, that is relevant
to quantum gravity.

So to me it seems inevitable to conclude that QC provides the larger context in which LQG progress
must be assessed. If one is to make a meaningful assessment, that is.

Now something I did not expect has happened. The Group Field Theory (GFT) program has come out with a way to do GFT cosmology. This could have a significant effect on the Loop program.

http://arxiv.org/abs/1303.3576
Cosmology from Group Field Theory
Steffen Gielen, Daniele Oriti, Lorenzo Sindoni
(Submitted on 14 Mar 2013)
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a non-linear and non-local extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semi-classical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
5 pages

 

[marcus]

Since I last posted on this thread two important papers have come out, one by Ashtekar and the other by George Ellis, Reza Tavakol, Tim Clifton. Both have to do with cosmology which is pretty clearly turning out to be the main arena for QG theory. Early universe cosmology, in particular, is a kind of testing ground for Loop gravity. Several of the recent posts on this thread have been on the general them of LQG and cosmology.

What Ashtekar here calls "Planck regime" is in other papers he cites specified to be "pre-inflationary" expansion history arising from the LQG bounce.
The George Ellis paper is interesting because of the whole gravitational entropy issue.
there are conceptual difficulties with defining the entropy of the gravitational field---IOW geometric entropy. There is in fact no agreed on idea of gravitational entropy. So one cannot say what happens to the entropy during the LQG bounce. the concept (which is probably observer-dependent and scale-dependent) fails to be defined. So Ellis paper is much needed:it attacks this problem of defining entropy.

http://arxiv.org/abs/1303.5612
A Gravitational Entropy Proposal
Timothy Clifton, George F R Ellis, Reza Tavakol
(Submitted on 22 Mar 2013)
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel-Robinson tensor, which has a natural interpretation as the effective super-energy-momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein-Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson-Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein's field equations. It is also in keeping with Penrose's Weyl curvature hypothesis.
17 pages

Ashtekar's paper is more of a review of recent progress in pre-inflation LQG cosmology and consequent opportunities to make testable predictions about features of the cosmic microwave background.

http://arxiv.org/abs/1303.4989
Loop Quantum Gravity and the The Planck Regime of Cosmology
Abhay Ashtekar
(Submitted on 20 Mar 2013)
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects, such as a modification of the consistency relation involving the scalar and tensor power spectra and a new source for non-Gaussianities. Thus, the genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations in the Planck regime. This report provides a bird's eye view of these developments for the general relativity community.
23 pages, 4 figures. Plenary talk at the Conference: Relativity and Gravitation: 100 Years after Einstein in Prague. To appear in the Proceedings to be published by Edition Open Access. Summarizes results that appeared in journal articles [2-13]

 

[torsten]

Yes, I totally agree that the falsification of a quantum gravity theory can be done by using cosmology. But also I agree with Tom that the grounded principles are not based on experimental results. During the birth of quantum mechanics, there was a close relationship between teory and experiment. One part of interpretational problems are caused by this history. Another part is reflected in the trial to define quantum geometry. Simple questions like: does the quantum geometrical state (for instance the superposition of spin networks) actually exists? are not answered. But an aswer would be important to go on.
But back to this topic...
In particular, a quantum gravity theory should explain the exponential increase of inflation. But I don't say any really good result in this direction (which satisfied me).
BTW, we formulated an inflation scenario (which purely geometrical roots) which is able to explain the exponential increase. In particular, the factor can be explicitly calculated using topological invaraints of the three manifold only. Maybe a beginning?

 

[marcus]

BTW, we formulated an inflation scenario (which purely geometrical roots) which is able to explain the exponential increase. In particular, the factor can be explicitly calculated using topological invariants of the three manifold only. Maybe a beginning?

That sounds intriguing! Maybe you should give a link to the paper. I cannot remember all the papers and the interesting results that come out of your alternative smooth structures approach.

In particular, a quantum gravity theory should explain the exponential increase of inflation.

Just to review, Loop bounce cosmology does have a brief period of faster than exponential expansion, which happens inevitably as a consequence of the bounce. It naturally occurs and then naturally ends as the density declines. It is called "super-inflation" because the scale factor goes as e^Ht with H increasing.

In ordinary inflation the scale factor goes as e^Ht with H approximately constant or slowly decreasing.

But this period of super-inflation does not continue long enough, according to the LQC calculations. So the researchers have had to assume the existence of a scalar field which could take over from the naturally occurring super-inflation and serve as an "inflaton" field, to finish the job.

A recent paper about that:

http://arxiv.org/abs/1301.1264
Inflation as a prediction of loop quantum cosmology
Linda Linsefors, Aurelien Barrau
(Submitted on 7 Jan 2013)
Loop quantum cosmology is known to be closely linked with an inflationary phase. In this article, we study quantitatively the probability for a long enough stage of slow-roll inflation to occur, by assuming a minimalist massive scalar field as the main content of the universe. The phase of the field in its "pre-bounce" oscillatory state is taken as a natural random parameter. We find that the probability for a given number of inflationary e-folds is quite sharply peaked around 145, which is indeed more than enough to solve all the standard cosmological problems. In this precise sense, a satisfactory inflation is therefore a clear prediction of loop gravity. In addition, we derive an original and stringent upper limit on the Barbero-Immirzi parameter. The general picture about inflation, super-inflation, deflation and super-deflation is also much clarified in the framework of bouncing cosmologies.
6 pages, 4 figures

 

[torsten]

Thanks for the paper. I understand the necessarity to introduce this scalar field but this field is not an output of the model.

That sounds intriguing! Maybe you should give a link to the paper. I cannot remember all the papers and the interesting results that come out of your alternative smooth structures approach.

Here is the link:
http://arxiv.org/abs/1301.3628
of the paper "On the origin of inflation by using exotic smoothness". It also explained the reason to introduce the scalar field.

 

[marcus]

...
Here is the link:
http://arxiv.org/abs/1301.3628
of the paper "On the origin of inflation by using exotic smoothness". It also explained the reason to introduce the scalar field.

It is an intriguing paper. Can you give me the most basic intuition of how a transition to an alternative differential structure can cause inflation? Intuitively what causes the inflation and then what causes it to stop?

 

[torsten]

It is an intriguing paper. Can you give me the most basic intuition of how a transition to an alternative differential structure can cause inflation? Intuitively what causes the inflation and then what causes it to stop?

In this paper we consider an exotic S^3 \times \mathbb{R}. This differential structure is characterized by a topological transition from a 3-sphere to another homology 3-sphere (for instance Poincare sphere) and back. Here we choose a homology 3-sphere \Sigma with a hyperbolic structure (i.e. negative scalar curvature). Then we have a change from a positive curvature (3-sphere) to a 3-manifold with negative curvature (looking like a 3-sphere).
This transition leads to an accelaerated expansion. But we were able to show more. The 4-manifold representing the transition also carries a hyperbolic structure leading to an exponential increase (two geodesics in a hyperbolic geometry diverge exponentially). This exponential increase can be also expressed explicitly: there is a tree with an exponential number of states.
We obtained also an effective picture for this transition: it can be described by a SU(2)-valued scalar field (inflanton).
Again: S^3 \rightarrow\Sigma \rightarrow S^3 are the transitions, the first transition leads to an accelerated expansion whereas the second transition stops it.
I hope it helps. My view is more geometrically.

 

[marcus]

Thanks Torsten! That does help.

I should mention in connection with new developments in LQG that the ILQGS blog has a wide-audience article by Mano Alesci and Francesco Cianfrani about their (quantum) Reduced LQG
approach to cosmology.
http://ilqgs.blogspot.com/2013/03/reduced-loop-quantum-gravity.html

It makes a bridge between the full LQG theory and cosmology because the reduction to the homogeneous and isotropic case is done within LQG
In conventional LQC the reduction is done first, and then this is reduced model is quantized, so the connection with the full theory is not so direct.

As I recall Jon Engle also has some recent work along these lines. It is very important because cosmology is the main testing ground for QG. We have to know what the full LQG theory has to say about the CMB power spectrum, conditions around the start of expansion, and the subsequent inflation.

The blog post by Alesci Cianfrani gives motivation and intuitive understanding of their new (reduced) version of Loop gravity.

 

[marcus]

In four days Wolfgang Wieland will give an ILQGS talk (available online) on a Hamiltonian approach to Spin Foam QG. This has been an important outstanding problem, how to unite the covariant Spin Foam approach with the older canonical LQG Hamiltonian approach.

Revised ILQGS Spring 2013 Schedule
http://relativity.phys.lsu.edu/ilqgs/

DATE	Seminar Title	                    Speaker 	     Institution
Jan 29 [B]Entanglement in loop quantum gravity[/B] Eugenio Bianchi  Perimeter Institute
Feb 12 [B]Dynamical chaos and the volume gap [/B]  Hal Haggard	     CPT Marseille
Feb 26 [B]Gravity electroweak unification[/B]	    Stephon Alexander Dartmouth College
Mar 12 [B]Quantum reduced loop gravity[/B]	    E.Alesci/F.Cianfrani Univ. Erlangen 
Mar 26 [B]Bianchi-I LQC,Kasner shift&inflation[/B] Brajesh Gupt     LSU
Apr  9 [B]Hamiltonian spinfoam gravity[/B]         Wolfgang Wieland CPT Marseille
Apr 23 TBA                                  Martin Bojowald  Penn State	
May  7 [B]Emergence of BF theories and gravi-weak Plebanski models from spinors[/B]
					    Antonino Marciano Dartmouth College

Wolfgang's paper of the same title, that the talk will be based on, is currently the leading paper on our first quarter 2013 MIP poll. https://www.physicsforums.com/showthread.php?t=681598

http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. ... Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures

 

[marcus]

Wolfgang Wieland's talk at ILQGS was given today and both the slides PDF and the audio are already online.
http://relativity.phys.lsu.edu/ilqgs/
I still do not see anyone single clear direction in how LQG+Spinfoam theory is developing. It seems necessary to keep alert to several possible directions. To me personally the line taken by Wieland and Speziale and others (see the short bibliography at the end of Wolfgang's talk) looks very promising. It is aimed directly at showing the CONSISTENCY of the theory and they seem to have made good progress.

On the other hand we saw in fourth quarter 2012 a lot of work being done with TENSOR models. Some ILQGS talks were given on tensorial QG. And today a relevant paper by Razvan Gurau appeared on arxiv. So I should post that as instance of either a closely related rival approach (GFT) or as a reformulation that is brewing.

http://arxiv.org/abs/1304.2666
The 1/N Expansion of Tensor Models Beyond Perturbation Theory
Razvan Gurau
(Submitted on 9 Apr 2013)
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges.
As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N to infinity limit, in the universality class of Gaussian tensor models.
45 pages

Gurau's paper is entirely technical. He refers to application in Quantum Gravity (e.g. via GFT) but does not give any detail. He proves many theorems. Past experience of both Gurau and Rivasseau work makes me expect that this may have significance for QG applications but I cannot foresee the specifics. Maybe some other people can.

 

[marcus]

A propos the preceding post, Razvan Gurau is to be one of the invited plenary speakers at the upcoming Loops conference, as is also Vincent Rivasseau. Loops 2013 will be held at Perimeter in latter half of July, just three months off, and I still have only a very rough notion of what the current state of LQG is that will appear at the biennial conference. There seem to be an unusually large number of different currents. We can watch the seminar talks at Perimeter, and at the ILQGS, during the run-up to the conference, for hints as to what the main developments are. Here are a couple of April talks scheduled at Perimeter:

The first of these seems unusual. An imaginary part of the action?
April 18, Yasha Neiman:
http://www.perimeterinstitute.ca/seminar/imaginary-part-gravitational-action-and-black-hole-entropy
THE IMAGINARY PART OF THE GRAVITATIONAL ACTION AND BLACK HOLE ENTROPY
I present a candidate for a new derivation of black hole entropy. The key observation is that the action of General Relativity in bounded regions has an imaginary part, arising from the boundary term. The formula for this imaginary part is closely related to the Bekenstein-Hawking entropy formula, and coincides with it for certain classes of regions. This remains true in the presence of matter, and generalizes appropriately to Lovelock gravity. The imaginary part of the action is a versatile notion, requiring neither stationarity nor any knowledge about asymptotic infinity. Thus, it may provide a handle on quantum gravity in finite and dynamical regions. I derive the above results, make connections with standard approaches to black hole entropy, and speculate on the meaning of it all. Implications for loop quantum gravity are also discussed.

April 25, Casey Tomlin:
http://www.perimeterinstitute.ca/seminar/loop-quantization-weak-coupling-limit-euclidean-gravity
LOOP QUANTIZATION OF A WEAK-COUPLING LIMIT OF EUCLIDEAN GRAVITY
I will describe recent work in collaboration with Adam Henderson, Alok Laddha, and Madhavan Varadarajan on the loop quantization of a certain G_N→ 0 limit of Euclidean gravity, introduced by Smolin. The model allows one to test various quantization choices one is faced with in loop quantum gravity, but in a simplified setting. The main results are the construction of finite-triangulation Hamiltonian and diffeomorphism constraint operators whose continuum limits can be evaluated in a precise sense, such that the quantum Dirac algebra of constraints closes nontrivially and free of anomalies. The construction relies heavily on techniques of Thiemann's QSD treatment, and lessons learned applying such techniques to the loop quantization of parameterized scalar field theory and the diffeomorphism constraint in loop quantum gravity. I will also briefly discuss the status of the quantum constraint algebra in full LQG, and how some of the lessons learned from the present model may guide us in that setting.

http://www.perimeterinstitute.ca/events/scientific-events

The Yasha Neiman talk relates to this March 2013 paper:
http://arxiv.org/abs/1303.4752
Imaginary action, spinfoam asymptotics and the 'transplanckian' regime of loop quantum gravity
Norbert Bodendorfer, Yasha Neiman
(Both authors recently took postdocs at Penn State.)

The Casey Tomlin talk relates to several recent papers:
http://arxiv.org/abs/1204.0211
Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I
Adam Henderson, Alok Laddha, Casey Tomlin

http://arxiv.org/abs/1210.3960
Constraint algebra in LQG reloaded : Toy model of an Abelian gauge theory - II Spatial Diffeomorphisms
Adam Henderson, Alok Laddha, Casey Tomlin

http://arxiv.org/abs/1210.6869
Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
Casey Tomlin, Madhavan Varadarajan
(Again for the most part the authors are full or part-time connected with Ashtekar's institute at Penn State, but also have ties with MPI-Potsdam, RRI-Bangalore, CMI-Chennai.)

 

[negativzero]

Smolin is a relativist and i love him, and i love quantizing space, and time, yes! But gravitons? Please! Show me one!
.
As far as I'm concerned it's a toss up as to whether gravity is a feature of vacuum energy or some kind of boson that goes between masses.
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After all, inertia inherited from inflation powered the early bang. That's a feature of spacetime, and some say, the vacuum energy. The Casimir effect is also a feature of spacetime [some would say it's exclusively electromagnetic], and vacuum energy. Another expansionary feature of spacetime is referred to as "dark energy." It seems entirely reasonable that gravity is a feature of vacuum energy too. You might call it, the "anti-expansion force."
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In such a case there would still be quantum descriptions but it would amount to a superposition of forces created by the vacuum resulting in a "vapor pressure" on masses. This would simultaneously empty out voids and create galaxy clusters.
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i'm reminded of Occam's razor. Why use 4 forces when you can use 3?
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i've never understood why relativity somehow assumes the graviton. It's just an assumption as far as i can tell.
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If the LQG folks are trying to quantize "defacto" gravitons, fine. Bless them!
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But I'm betting my mana that there is no single unique boson identifiable as a graviton.
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Yes, i know Friedman and Einstein early on looked to see if gravity was caused by vacuum energy and calculated something like 10^128 times TOO MUCH energy and essentially shelved the idea. My understanding of today's thinking is that the existence of other energy from different places "cancels" this enormous vacuum energy, as a result of superposition. That just means the subject is still open.
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[marcus]

...
If the LQG folks are trying to quantize "defacto" gravitons, fine. Bless them!
...

That's a good word for it. The graviton arises in quantizing perturbations of flat geometry, so to get their hands on gravitons the LQG folks restrict the boundary of a spacetime region in such a way as to approximate flatness.

You could say that gravitons are more native to a fixed background approach and not native to fully dynamic geometry. So a background independent non-perturbative approach like LQG has to use some arbitrary restrictions just to make them "exist". They are, one could say, only "de facto"

Registration for Loops 2013 (late July, still 3 months off) has been remarkable.
The website now has announced:
Due to overwhelming response, registration for this conference will close on Wednesday, May 1, 2013.
http://www.perimeterinstitute.ca/conferences/loops-13

The conference organizers have taken an interesting tack: mixing with other approaches, bringing together all kinds of background independent QG. It is worth reading their statement of purpose/philosophy. I do not remember seeing any Loop conference organizer statement quite this open-to-all-QG, and I've been watching since 2004 when Rovelli hosted one at Marseille.
==quote Loops 3013==

Quantum gravity aims at unifying Einstein's vision of space-time as a dynamical object with the realization that fundamental physics and hence space-time has to be quantum. This opens up a large variety of research questions and directions, which range from foundational physical issues having to do with the nature of space and time, to current searches for experimental signatures of quantum spacetime.

This conference, which is part of the series of Loops conferences, will present and review recent progress and highlights in loop quantum gravity and other quantum gravity approaches. We will focus mainly on background independent approaches which are approaches that do not depend on perturbation theory formulated in a classical background.

Plenary talks will highlight the most important recent developments in quantum gravity research. Afternoon (parallel) sessions are open to contributed talks and will be focussed on particular topics or subfields and give room for discussions, exchange of ideas and a critical assessment of open questions.

The conference will bring quantum gravity researchers from all over the world together and we also hope to share the excitement of quantum gravity research with participants from other research fields.
==endquote==

 

[negativzero]

Thx marcus. This is a fine thread. i may never catch up to you guys.
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You wrote, in part: "...background independent non-perturbative approach like LQG has to use some arbitrary restrictions just to make them "exist"..."
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So they need to constrain the edges of their space such that stuff propagates in a tidy parallel manner?
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i assume the perspective of the point-like observer is not sufficient to constrain boundaries, because somebody else would have said so already. What about the particle sphere? A coordinate system where the surface of an expanding sphere is the "origin?" i guess the question I'm getting at would be whether simply changing coordinate systems makes any sense as an "arbitrary restriction?" Or do the restrictions have to act to describe event generation on an individual basis for each particle or bit of momentum?
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Your comments are always welcome.
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[marcus]

...So they need to constrain the edges of their space such that stuff propagates in a tidy parallel manner?... i guess the question I'm getting at would be whether simply changing coordinate systems makes any sense as an "arbitrary restriction?"
...

"Graviton propagator" work was carried out in 2005-2007...
Here is a 2007 paper---not to read, it's too technical and has no diagrams. But it's a kind of landmark from which to work backwards in time. The more conceptual stuff (with diagrams) came a year or two earlier, and hit a technical snag. Then modifications in the "vertex" formula, which goes into calculating transition amplitudes, overcame that difficulty.

http://arxiv.org/abs/0711.1284
The complete LQG propagator: II. Asymptotic behavior of the vertex
Emanuele Alesci, Carlo Rovelli
(Submitted on 8 Nov 2007)
In a previous article we have show that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit.
Comments: 16 pages

What I have to find are simpler more conceptual papers with diagrams that give an intuitive idea of how they are going after the graviton "two-point function" or propagator: the amplitude of going from point A (on the region's boundary) to point B(also on the boundary).
This should show an inverse-square dependence, in line with the Newtonian inverse square law.
I'll look.
EDIT: still no success

 

[negativzero]

marcus, I've only read:
http://arxiv.org/pdf/0711.1284v1.pdf

once, but i think i get the general picture.
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We are talking about the "graph paper" of the micro reality, where time and space are parceled out into their smallest bits. This article is about the smallest bits of gravity. Vertices are like events or particle interactions, and edges of the geometry are called "propagators" and are like force carriers.
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Forgive me if i sound impartial, but i have been a fan of a simple 3D tetrahedral structure for decades, perhaps because, well, it's simple!
Now the LQG gang are trying to force 5 simplex tetrahedons my down my brain! Okay, they seemed to have dumbed down the geometry with intertwining or something to 4 simplex with a slight asymmetry. And, "...That is, the spin-intertwiner correlations are just functions of the spin-spin correlations for a state with this symmetry! The intertwiner dependence drops out! This means that the propagator is completely unaffected from the correlations involving the intertwiners...," but they definitely lose me, anyway.
...
In this algebra gravitons are like phonons in a tuba?:
"...In doing so, we have also learned several lessons. The main lesson is that the non-commutativity
of the angles requires a semiclassical state to have an oscillatory behavior in the intertwiners. In
order to match this behavior, and approximate the semiclassical dynamics, the vertex must have a
similar oscillatory dependence on the intertwiners. (This should not affect with possible finitness
properties of the model [15].) The second lesson is that the symmetries of the boundary state must
be considered with care, if we do not want to loose relevant dynamical information. Symmetrizing
over the permutation of the vertices is a simple way of achieving a symmetric state without inserting
additional unwanted symmetries..."
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Another thing, it's trivial, i suppose, "...Using this technique, we have found in a previous paper [4]
that the definition of the dynamics of loop quantum gravity (LQG) by means of the Barrett-Crane
(BC) spinfoam vertex [5] fails to give the correct tensorial structure of the graviton propagator in the
large-distance limit..." If it was MY pet theory, and i wanted some comment i might try to work the numbers and come up with dark energy coming out of the same math.
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Thanks, and please feed me more. One day i'll get it.
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[Solkar]

You could say that gravitons are more native to a fixed background approach and not native to fully dynamic geometry. So a background independent non-perturbative approach like LQG has to use some arbitrary restrictions just to make them "exist". They are, one could say, only "de facto"

Hi gents!

I do not intend to mingle into your expert discussion, but could you pls explain in brief what substitutes the systematic "role" of gravitons as quanta in LQG?

Rovelli's "quanta of area" and "quanta of space"?

Solkar

 

[marcus]

I think the basic aim in LQG, and any sort of NON-perturbative QG, is to be able to calculate transition amplitudes between initial/final boundary states of geometry.

Boundary states of geometry are determined by some number of geometric measurements made before/during/after at the boundary of some spacetime region, they may be relations among quantities, involve matter, etc. May involve measuring angles and, as you suggested, area and volume.

I think the essential quantum nature of geometry is not that geometry is "made of little bits" but that the operators representing geometric measurements should have discrete spectrum and not necessarily commute. It is not about what Nature is "made of" but rather about how she responds to measurement. And about transition amplitudes.

I hardly need to say this, but no need to be overly modest about (non)expertise, Solkar. Some here are involved in professional research but others are just watching from the sidelines. I'm an interested onlooker. Correct me if I'm wrong (anyone) but I think gravitons arise in the mathematics when it is done on a fixed rigid geometry. They are perturbations (ripples on a fixed background geometry.) I don't think we assume that nature works like that. We assume she's basically NON-perturbative and that geometry is fully dynamic and fully interacting with matter. So we don't presume gravitons have a real existence even though they are mathematically very convenient in certain types of analysis.

 

[marcus]

Solkar, Bee Hossenfelder, a quantum gravity phenomenologist, and one of the best communicators about QG as well, just put up on her blog a splendid essay:
http://backreaction.blogspot.com/2013/04/listen-to-spacetime.html

It suggests another way to think about what non-perturbative quantum gravity is doing.

She cites work by Alain Connes and coworkers, and also some fairly new work by Achim Kempf.

(Although she does not say so explicitly) I think one could fit the LQG/Spinfoam approach into this paradigm of what QG is attempting.

 

[negativzero]

i'm neither athlete nor paying fan in this stadium...just peeking through a hole in the fence.
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Why doesn't Time zero create a "fixed background geometry?" And why not pick the particle sphere, event sphere, or "known universe" of some arbitrary particle to establish background?
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It would seem like taking gravitons as infinite in extent would discourage a lot of background assumptions.
But these are relativists and they are stubborn stock. So they like to use Lagrangian operators and point out that General Relativity doesn't necessarily conserve energy.
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And finally, if timezero is a boundary then perhaps the present too could be one.
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[Solkar]

@Marcus: Thx a lot! I'll have to ponder over that a little.

i'm neither athlete nor paying fan in this stadium...just peeking through a hole in the fence.

I'd copy that.

iWhy doesn't Time zero create a "fixed background geometry?" And why not pick the particle sphere, event sphere, or "known universe" of some arbitrary particle to establish background?

Just a wild guess - maybe because the notion of sth like a "sphere" already needs a geometry to be meaningful?