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Reformulation of Loop gravity in progress, comment?

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marcus
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Jan29-13, 03:06 PM
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Bianchi's slides http://relativity.phys.lsu.edu/ilqgs/bianchi012913.pdf are exceptionally clear, visual, and conceptually intuitive.
"Entanglement and the Bekenstein-Hawking entropy"
The B-H entropy is explained simply as the entang. entropy between the two regions

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

I just checked the audio link http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav and that part is not yet online.
marcus
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Jan31-13, 01:55 AM
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The audio for Bianchi's 29 Jan ILQGS talk has been posted:
http://relativity.phys.lsu.edu/ilqgs/bianchi012913.wav

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

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

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

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

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

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

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

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

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

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

http://arxiv.org/abs/1301.5859
Hamiltonian spinfoam gravity
Wolfgang M. Wieland
(Submitted on 24 Jan 2013)
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
28 pages, 2 figures
marcus
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Feb3-13, 11:18 PM
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The papers of Engle and by Alesci Cianfrani mentioned in above post indicate that Loop cosmology can be embedded in the full LQG theory, or derived from it. Reductions to the interesting cases for cosmology can be done AFTER the quantum theory is constructed. It has been pointed out that this opens the way for testing the full LQG theory. It has to give the right answers about the early universe.

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

The main actively researched QG rival to LQG in modeling the early universe has been the Asymptotic Safe QG program. String and Causal Dynamical Triangulations don't seem to have much to say about the start of expansion---or at least not much is being written from those perspectives.
However, the AS program may have experienced a severe setback with the appearance of Hamber's result that a QG theory in which the cosmological constant runs cannot be general covariant. For some discussion:
http://www.physicsforums.com/showthread.php?t=668612
tom.stoer
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Feb25-13, 12:01 AM
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Marcus, what about some kind of "status report" of LQG?

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

What do you think? Where are the main results and what are the key issues?
marcus
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Feb25-13, 12:52 PM
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Quote Quote by tom.stoer View Post
Marcus, what about some kind of "status report" of LQG?

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

What do you think? Where are the main results and what are the key issues?
That's a nice question. I will have to respond in several stages. First, a general introduction, the overall context, how LQG fits into the picture, where I think it's going.

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

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

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

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

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

This is why I think it is so important to review Marciano's May 2012 talk, and to hear Alexander's talk tomorrow (26 February 2013).
marcus
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Feb25-13, 01:25 PM
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As I see it, LQG is a subfield of LQC. Much (perhaps most) Loop community work is now Cosmo-related. Papers by Engle and by Alesci show a good bridge, symmetry reduction can be done at the quantum level. And symmetry restrictions are gradually being relaxed--eg the work on Bianchi-One cosmologies.

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

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

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

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

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

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

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

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

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

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

EDIT: Reminder, the link to get slides PDF and audio for tomorrow's talk by Alexander is
http://relativity.phys.lsu.edu/ilqgs/
The title of the talk is Gravity Electroweak Unification
marcus
#151
Feb26-13, 03:49 PM
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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&a...=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
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Feb26-13, 04:32 PM
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Marcus, my question was about LQG as the general framework, not about LQC.
marcus
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Feb26-13, 04:35 PM
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Quote Quote by tom.stoer View Post
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
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Feb26-13, 05:00 PM
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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
#155
Feb26-13, 05:00 PM
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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
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Feb27-13, 02:14 AM
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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
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Feb27-13, 12:45 PM
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Quote Quote by tom.stoer View Post
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
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Feb27-13, 04:45 PM
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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
#159
Feb28-13, 09:48 PM
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Quote Quote by tom.stoer View Post
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
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Mar15-13, 01:12 PM
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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:
Quote Quote by marcus View Post
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
#161
Mar25-13, 01:26 AM
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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
#162
Mar26-13, 03:39 PM
P: 73
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?


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