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Clear concise Loop survey as of January 2012

by marcus
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atyy
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Jan31-12, 10:53 PM
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Quote Quote by marcus View Post
Here's a recent paper by Etera Livine and a co-author in Dittrich group at AEI, Meché Martin-Benito.
http://arxiv.org/abs/1111.2867
Classical Setting and Effective Dynamics for Spinfoam Cosmology
The development of spinfoam approach to cosmology is just beginning. Still at rudimentary toymodel stage. This paper is probably the most recent window on these beginnings.
It reminds me that the boundary can be disconnected. It can consist of an initial state and a final state.
Offhand I don't see how this can deal with anything but a spatially finite universe like hypersphere S3 or 3-torus T3. One would pick some arbitrary interval of time like from one minute before bounce to one minute after bounce. And fix some initial and final quantum states of geometry----initial and final spin network states.

Then the boundary consists of two disconnected components. And the bulk is spinfoam histories that bridge between initial and final. That picture is more aligned with the "transition amplitude" language.
Thanks! I'll read it.

Quote Quote by Karmerlo View Post
Thanks a lot. And I have another question: is there any good and easy-to-read reference on Hamilton Constraint? I checked some Thiemann's paper, like Quantum Spin Dynamics series, which is very hard to follow? I wish I could hear from your recommendation. Thanks.
Quote Quote by marcus View Post
3. A straightforward approach that might provide an introduction to the OLD (Thiemann) version of the Loop Hamiltonian? This would work if you are near a college or university and can use the library. If they don't have this textbook, suggest they get a copy! The section on the Hamiltonian constraint is pages 117-123.
http://www.amazon.com/First-Course-L.../dp/0199590753
A First Course in Loop Quantum Gravity
Rodolfo Gambini, Jorge Pullin
Oxford University Press.

I haven't looked at the Gambini Pullin textbook myself so I can't reliably recommend. But as a first course text for advanced undergrads it shouldn't be too dense. You could browse a library/bookstore copy without buying, to be sure. I'll keep thinking about this, Karmerlo, and may have something more in a day or two. Also others perhaps with a completely different point of view, may have suggestions!
Another introduction to the Thiemann Hamiltonian is
http://arxiv.org/abs/1007.0402
Introductory lectures to loop quantum gravity
Pietro Doná, Simone Speziale
marcus
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Jan31-12, 10:59 PM
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Quote Quote by atyy View Post

Another introduction to the Thiemann Hamiltonian is
http://arxiv.org/abs/1007.0402
Introductory lectures to loop quantum gravity
Pietro Doná, Simone Speziale
Hey and that one is free online! (The textbook is rather pricey.) Good thought.
tom.stoer
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Feb1-12, 12:13 AM
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Unfortunately you will not find new developments like Rovelli's http://arxiv.org/abs/1005.0817 in http://arxiv.org/abs/1007.0402. Then there are a couple of papers from Thiemann published in spring 2011 not covered in http://arxiv.org/abs/1007.0402, but I have to admit that I haven't studied them in detail, so I can't comment on their relevance in this context.

I would say that everybody agrees that there is no unique regularized quantum Hamiltonian constraint. In addition there is not even a treatment of all constraints on equal footing (Gauss law and diffeomorphism constraints are solved in the spin network basis). Whether the Hamiltonian constraint is (A) only a technical issue or (B) really the tip of an iceberg (canonical approach as starting point, partial gauge fixing, wrong or ineqivalent connection variables, second class constraints, anomalies, discretization, regularization, ...) is currenly not known.

Personally I think it's (B)


There are a couple of papers discussing certain aspects of the problem, especially Alexandrov's analysis published in 2010. I started a thread on these issues here http://www.physicsforums.com/showthread.php?t=570007

I would say that one can agree one the problems Alexandrov discusses, even if not everybody will agreee on his proposals for a solution (which have not yet provided any concrete results as far as I can see)
marcus
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Feb1-12, 12:15 PM
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just to remind everybody, we're taking Ashtekar's recent survey as an opener for discussion of the overall Loop gravity situation.
Loop underwent a revolution 2007-2009 which led to a NEW SPINFOAM FORMULATION IN 2010-2011.
This is found in explicit, definitive form on page 13 of the Zakopane lectures. (If you have an old copy it's on page 9.)
This is the formulation using the map fγ from functions on SU(2) to functions on SL(2,C).
What I see now is a bunch of people converging on the problem of finding a corresponding Hamiltonian formulation. There is a lot of activity around this.

==quote post #17==
... to find out about the Loop Gravity UNSETTLED HAMILTONIAN SITUATION.
As far as I know (AFAIK) there is no Hamiltonian at present, only several proposals.
They have not been fully worked out.
...
First, I can give some indication of the unsettled situation by linking to some technical papers ...
Laurent Freidel is certainly someone to watch and he and Valentin Bonzom have one:
http://arxiv.org/abs/1101.3524
The Hamiltonian constraint in 3d Riemannian loop quantum gravity
"...This fills the gap between the canonical quantization and the symmetries of the Ponzano-Regge state-sum model for 3d gravity."

Carlo Rovelli and Alesci have one:
http://arxiv.org/abs/1005.0817
A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
"...The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearence of the 15j Wigner symbol in these."

Etera Livine and Valentin Bonzom have one:
http://arxiv.org/abs/1110.3272
A new Hamiltonian for the Topological BF phase with spinor networks
"...We introduce a new scalar Hamiltonian, based on recent works in quantum gravity and topological models, which is different from the plaquette operator..."

It's really important that the Hamilton be graph-changing, and e.g. be capable of a 1-to-4 Pachner move. Space can expand by giving birth to new vertices. I don't understand how this deficiency persisted so long. It's a good sign that the 15j Wigner symbol shows up (basic to spinfoam dynamics). ...
....
In addition to those three, there is also another Hamilton proposal from Etera Livine, Daniele Oriti, and James Ryan
http://arxiv.org/abs/1104.5509
Effective Hamiltonian Constraint from Group Field Theory
"...Our strategy is to expand group field theories around non-trivial classical solutions and to interpret the induced quadratic kinematical term as defining a Hamiltonian constraint on the group field and thus on spin network wave functions..."
==endquote==
marcus
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Feb1-12, 12:39 PM
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Whether it turns out to be right or wrong, in accord with Nature or not, the 2011 formulation is definite and explicit. It basically fits on one page--page 13 of the Zako lectures
http://arxiv.org/abs/1102.3660. Indented quote:
Let me now come to the main point of these lectures: the definition of the partition function of 4d Lorentzian LQG. This is defined by
ZC = Ʃjf,vef(2jf +1) ∏vAv(jf,ve), (67)
where C is a two-complex with faces f, edges e and vertices v, the intertwiners ve are in the space Ke = Kjf1 ...jfn where f1 , ..., fn are the faces meeting at the edge e and
Av(jf,ve) = Tr[⊗e∈v(fγve)]. (68)
where fγ is given in (54) and γ is a dimensionless parameter that characterizes the quantum theory, called Immirzi, or Barbero-Immirzi, parameter. This is the definition of the covariant dynamics of LQG.
Notice that the theory is entirely determined by the imbedding Yγ of SU(2) functions into SL(2,C) functions, defined in section IIIA, see equation (50). An intuitive track for understanding what is happening is the following. If we erase fγ in (68) we obtain the Ooguri quantization...
Pretty clearly progress here is like walking on two feet. We have a definitive SF formulation and now the game is to discover the associated Hamilitonian. My guess is one will appear within about 2 years, by 2014 maybe sooner. Because I see smart creative research going on, and interest seems to be heating up around this. The process of deciding on a Hamiltonian version of LQG may in turn cause a modification of the SF formulation that we see here. That's how walking works

INCIDENTAL INFORMATION: Most of us are aware of Louis Crane's idea for putting SM matter on quantum geometry. Here's a thread about it:
http://physicsforums.com/showthread.php?t=564867
I notice it's getting some recognition. Check out this conference announcement:
http://www.fctec.ualg.pt/qisg/speakers.html
The QG speaker lineup (to be confirmed) includes Laurent Freidel, John Barrett, Louis Crane.
Also John Madore of University Paris-Sud (the Orsay branch where Rivasseau is, also Aristide Baratin)
Here's a list of his papers (noncommutative geometry/gravity)http://arxiv.org/find/grp_physics/1/.../0/1/0/all/0/1


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marcus
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Feb2-12, 01:32 PM
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I want to see how this paper fits in to the overall picture. The conclusions here are quite new to me, maybe someone can comment.

http://arxiv.org/abs/1201.5423
Dirac fields and Barbero-Immirzi parameter in Cosmology
G. de Berredo-Peixoto, L. Freidel, I.L. Shapiro, C.A. de Souza
(Submitted on 26 Jan 2012)
We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state p = wρ, with w = 1 which is independent of the BI parameter. The existence of mass imposes a variable w, which creates either an inflationary phase with w=-1, or assumes an ultra hard equation of states w = 1 for very early universe. Both phases relax to a pressureless fluid w = 0 for late universe (corresponding to the limit m→∞).
16 pages

I may as well say from the broadest perspective how I view Loop-and-allied QG. I think that for the past century the archetype for fundamental physics has been the hydrogen atom (and everything that followed from that) and that a new direction is emerging where the primary object of interest is the CMB sky. More generally one could include the (so far unmapped) Cosmic Neutrino Background which, if we could see it, would be a picture of a much earlier time. So for generality we could say CMB/CNB or just call it CBR for cosmic background radiation. A greatly magnified snapshot of early time--presumably with interaction occurring between quantum matter and geometry.

So I see fundamental physics veering off in a new direction where the archetypal thing you want to explain is the CBR skymap and the primary thing you want to model is the early universe. And I keep seeing people's different proposals for QG and ideas about how the early cosmos may have worked.

For instance, just this past week several papers by Wetterich presenting a new approach to QG. You can find the links in the bibliography if you haven't already checked them out and want to. There's a growing number of people focusing interest on this.

As one instance of this, I'd like to better understand the direction in Freidel's recent papers. Here they are:
http://arxiv.org/find/grp_physics/1/.../0/1/0/all/0/1
And here are the titles of the six most recent:

1. arXiv:1201.5470 [pdf, other]
New tools for Loop Quantum Gravity with applications to a simple model
Enrique F. Borja, Jacobo Díaz-Polo, Laurent Freidel, Iñaki Garay, Etera R. Livine
Comments: 4 pages, to appear in Proceedings of Spanish Relativity Meeting 2011 (ERE 2011) held in Madrid, Spain

2. arXiv:1201.5423 [pdf, ps, other]
Dirac fields and Barbero-Immirzi parameter in Cosmology
G. de Berredo-Peixoto, L. Freidel, I.L. Shapiro, C.A. de Souza
Comments: LaTeX file, 16 pages, no figures

3. arXiv:1201.4247 [pdf, ps, other]
On the relations between gravity and BF theories
Laurent Freidel, Simone Speziale
Comments: 16 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

4. arXiv:1201.3613 [pdf, other]
On the exact evaluation of spin networks
Laurent Freidel, Jeff Hnybida
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Geometric Topology (math.GT)

5. arXiv:1110.6017 [pdf, ps, other]
Dynamics for a simple graph using the U(N) framework for loop quantum gravity
Enrique F. Borja, Jacobo Diaz-Polo, Laurent Freidel, Iñaki Garay, Etera R. Livine
Comments: 4 pages. Proceedings of Loops'11, Madrid. To appear in Journal of Physics: Conference Series (JPCS)

6. arXiv:1110.4833 [pdf, ps, other]
Continuous formulation of the Loop Quantum Gravity phase space
Laurent Freidel, Marc Geiller, Jonathan Ziprick
Comments: 27 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
marcus
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Feb2-12, 11:45 PM
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Bee Hossenfelder and co-authors just posted an interesting new approach to QG phenomenology. Testing is a key element of the present situation, so I will quote their conclusion section.
http://arxiv.org/abs/1202.0412
Emission spectra of self-dual black holes
Sabine Hossenfelder, Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 2 Feb 2012)
We calculate the particle spectra of evaporating self-dual black holes that are potential dark matter candidates...

==quote Hossenfelder Modesto Prémont-Schwarz introduction and conclusion==
...
One approach to quantum gravity, Loop Quantum Gravity (LQG) [1–4], has given rise to models that allow to describe the very early universe. Simplified frameworks of LQG using a minisuperspace approximation has been shown to resolve the initial singularity problem [5, 6]. In the present work we will study the properties of black holes in such a minisuperspace model. The metric of black holes in this model was previously derived in [7], where it was shown in particular that the singularity is removed by a self-duality of the metric that replaces the black hole’s usually singular inside by another asymptotically flat region. The thermodynamical properties of these self-dual black holes have been examined in [8], and in [9] the dynamical aspects of the collapse and evaporation were studied.
...
...
4 Conclusion
We have derived here an approximate analytic expression for the emission spectrum of self-dual black holes in the mass and temperature limits valid for primordial black holes evaporating today. The idea that primordial black holes are dark matter candidates is appealing since it is very minimalistic and conservative, requiring no additional, so far unobserved, matter. This idea has therefore received a lot of attention in the literature. However, the final stages of the black hole evaporation seem to be amiss in observation, and so there is a need to explain why primordial black holes were not formed at initial masses that we would see evaporating today. The self-dual black holes we have studied here offer a natural explanation since they evaporate very slowly. The analysis we have presented here allows to calculate the particle flux from such dark matter constituted of self-dual black holes, and therefore is instrumental to test the viability of this hypothesis of dark matter constituted of self-dual black holes against data.
==endquote==
tom.stoer
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Feb3-12, 12:10 AM
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Quote Quote by marcus View Post
... the 2011 formulation is definite and explicit. It basically fits on one page ...

Pretty clearly progress here is like walking on two feet. We have a definitive SF formulation and now the game is to discover the associated Hamilitonian. My guess is one will appear within about 2 years, by 2014 maybe sooner.
I am not so optimistic.

It us still unclear if these constrants are implemented correctly in these SF models; it may very well be that this is NOT the case, which means that a CORRECT canonical quantization a la Dirac which you are hoping for will of course not re-create an INCORRECT SF model.
marcus
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Feb3-12, 01:16 PM
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Tom, you stress the issue of CORRECTNESS. That is inevitably speculative and governed by preconceptions based on what has been done in other fields in the past. This is fine, but I have not been talking about correctness. So let me recall to you what I said.
Quote Quote by marcus View Post
Whether it turns out to be right or wrong, in accord with Nature or not, the 2011 formulation is definite and explicit. It basically fits on one page--page 13 of the Zako lectures
http://arxiv.org/abs/1102.3660. Indented quote:
Let me now come to the main point of these lectures: the definition of the partition function of 4d Lorentzian LQG. ...
...
where fγ is given in (54) and γ is a dimensionless parameter that characterizes the quantum theory, called Immirzi, or Barbero-Immirzi, parameter. This is the definition of the covariant dynamics of LQG.
Notice that the theory is entirely determined by the imbedding Yγ of SU(2) functions into SL(2,C) functions, ...
Pretty clearly progress here is like walking on two feet. We have a definitive SF formulation and now the game is to discover the associated Hamilitonian. My guess is one will appear within about 2 years, by 2014 maybe sooner. Because I see smart creative research going on, and interest seems to be heating up around this. The process of deciding on a Hamiltonian version of LQG may in turn cause a modification of the SF formulation that we see here. That's how walking works
...
I have been trying to base discussion on objective facts--stuff I can observe--and on how I think an empirical mathematical science evolves.

I don't think it is our job to be optimistic or pessimistic about "correctness" and I think, e.g., that Bee Hossenfelder understands this. You should know that Modesto tweaked the Hamiltonian used in LQC in order to get his two-mouth Loop BH, with their slow evaporation.
I doubt that Bee believes or disbelieves in two-mouth Loop BH, but she recognizes the relevance to the dark matter problem and the desirability of TESTING. The test could discredit Modesto's tweak of the the Hamiltonian. Or it might even serve as a test of the LQC Hamiltonian itself. It is also a creative minimalist proposal for dark matter. Win lose up down--any way it goes is good. I think it is to some extent a waste of time to try to guess "correct" or not about things like this. If we ask a clear question, Nature may reply.

What I see is a heap of smart people piling up on various Loop and quantum universe problems right now. Part of that is a bunch of the best ones jumping on the Hamiltonian. Seeing that helps me draw conclusions about what to expect. (but not conclusions about "optimism" or "correct" )

The struggle is to get models of the early U and of BH which have clear mathematical definition, and then to test. This will guide us. This is the "walking" that I spoke about.
tom.stoer
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Feb3-12, 02:04 PM
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marcus, don't get me wrong; I am not talking about correctness of the model (in the sense of its agreement with nature), but about correctness of a mathematical procedure; unfortunately there are indications that SF models as of today are wrong in the second sense b/c certain aspects of constraint quantization are not taken into account properly

regarding tests: I agree that nature should be our guideline, but I think you understand that in the "deep QG regime" there are no tests available, therefore falsification (in the sense of Popper) may become meaningless to some extent; and unfortunately the mathematical problems will not show up in the semiclassical regime where tests may become available

therefore math should be a stronger guiding principle in QG (than e.g. in low-energy phenomenological models), not a weaker one

I don't say that Rovelli perspective is wrong, but it's definitly not the only one; there are different perspectives and approaches, and as long as we do not have a proof (!) that Rovelli's approach is correct in the first sense (!) we have to investigate alternatives as well (and this is what is done by other research groups as you certainly know)
marcus
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Feb3-12, 02:39 PM
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Quote Quote by marcus View Post
Tom, you stress the issue of CORRECTNESS. That is inevitably speculative and governed by preconceptions based on what has been done in other fields in the past...
Quote Quote by tom.stoer View Post
marcus, don't get me wrong; I am not talking about correctness of the model (in the sense of its agreement with nature), but about correctness of a mathematical procedure;...
Tom, I intended BOTH kinds of correctness including the preconceptions people have about what mathematical procedures are correct. These preconceptions are based on analogy with "what has been done in other fields in the past" and has been successful in the past.

You are a bit vague about "certain aspects of constraint quantization." How about focusing on the concise definition of spinfoam Loop gravity that I transcribed in post #23? Where is the trouble in that definition?

I have to go, but promise I will get back to this as soon as time permits.

I think the thing you might want to look at is the "shadow" map fγ, from functions on SU(2) to functions on SL(2,C). I call it shadow because it casts a shadow of the smaller thing into the larger and I need a name for it to bring attention, it is a key mapping.
tom.stoer
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Feb3-12, 02:47 PM
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Quote Quote by marcus View Post
Tom, I intended BOTH kinds of correctness including the preconceptions people have about what mathematical procedures are correct. These preconceptions are based on analogy with "what has been done in other fields in the past" and has been successful in the past.
Yes; and I strongly believe that especially the "mathematically correct implementation of constraints during quantization" is still of major importance; it's nearly as well established as "1+1=2" ...
marcus
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Feb3-12, 05:53 PM
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I think part of what you are talking about are strictly mathematical values. Clarity, consistency, rigorous proof... I too hold them in high regard.

Another part of what you seem to be saying is that every quantum theory should be the result of "quantizing" a classical theory according to a traditional procedure which you have in mind.

But wait, that doesn't seem reasonable. You can't mean that. I think you mean that Hamiltonian LQG should be the result of a traditional Dirac quantization of the classical theory. I'm not sure that is right, but it does not seem so radical so I want to let it pass for the moment.

In that case, if I understand you, the spinfoam QG which I gave the definition for in post #23 could be OK--it does not have to be the result of a "correct" quantization of classical relativity. It should be testable and have the right limits. What you are worrying about, then, would be the Hamiltonian formulation that we don't have yet. Is that it?

I would encourage you not to be worried about it until we actually see what the researchers come up with. Let's wait for them to sin first before we condemn them! A few posts back I mentioned people who seem to be interested in arriving at a post-2010 Hamiltonian formulation: Freidel, Geiller, Ziprick, Livine, Bonzom, Alesci, Rovelli, Ryan, Dittrich,... (I can't remember all the names.) I'm excited by this development, by all the new activity, and see no reason for us to start shaking our heads already.

BTW there's an excellent PIRSA video talk by Ziprick on the FGZ paper (Loop "classical" gravity ) that was just posted online:
http://pirsa.org/12020096/
atyy
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Feb3-12, 06:03 PM
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@tom.stoer, is this a correct interpretation of your concerns?

1. The EPRL model is supposed to match the state space of canonical LQG.

2. Every Lagrangian theory presumably has its canonical counterpart.

3. So if EPRL is consistent and matches canonical LQG, then the Hamiltonian constraint should exist.

4. If the Hamiltonian constraint doesn't exist, then EPRL could be a consistent quantum theory, but it would not be quantum general relativity in the loop variables (instead it could be a background independent formulation of string theory ).
marcus
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Feb4-12, 02:38 PM
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The Hossenfelder et al paper points out that the double primordial mini-BH idea of dark matter is appealing because minimalist and conservative. No exotic new particles needed to explain DM. I'll assemble the links as convenience if anyone wants to check it out:
S. Hossenfelder, L. Modesto and I. Premont-Schwarz, http://arxiv.org/abs/1202.0412
Emission spectra of self-dual black holes
L. Modesto, http://arxiv.org/abs/0811.2196
Space-Time Structure of Loop Quantum Black Hole
L. Modesto and I. Premont-Schwarz, Phys. Rev. D 80, 064041 (2009) http://arxiv.org/abs/0905.3170
Self-dual Black Holes in LQG: Theory and Phenomenology
S. Hossenfelder, L. Modesto and I. Premont-Schwarz, Phys. Rev. D 81, 044036 (2010) http://arxiv.org/abs/0912.1823
A model for non-singular black hole collapse and evaporation

======================================
EDIT: Since we just turned a page and I want to make Atyy's post #32 easier to refer to, I will copy it here:

Quote Quote by atyy View Post
@tom.stoer, is this a correct interpretation of your concerns?

1. The EPRL model is supposed to match the state space of canonical LQG.

2. Every Lagrangian theory presumably has its canonical counterpart.

3. So if EPRL is consistent and matches canonical LQG, then the Hamiltonian constraint should exist.

4. If the Hamiltonian constraint doesn't exist, then EPRL could be a consistent quantum theory, but it would not be quantum general relativity in the loop variables (instead it could be a background independent formulation of string theory ).
tom.stoer
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Feb4-12, 06:14 PM
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It's nearly correct, but it's not my concern

1. yes

2. yes

3. but EPRL isn't correct; nevertheless a related Hamiltonian can exist, but it's not the correct one

4. EPRL could be a reasonable theory, but does not correspond to canonical LQG

The problem is the following

a) in EPRL you start with classical BF theory and add simplicity constraints to get GR instead of BF; the way these simplicity constraints are implemented is wrong

b) in Ashtekar's complex variables you have to introduce a reality condition which results in seond class constraints; implementing them on physical states is wrong as well

a) and b) are closely related; the problem is that in both cases the constraints are second class, but this is treated incorrectly

So the problem is not "4. ... the Hamiltonian constraint doesn't exist" but that it's not the correct Hamiltonian; you have two quantization procedures, both are wrong, and now you show that they are equivalent; that doesn't help much ;-)
marcus
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Feb4-12, 08:23 PM
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Quote Quote by tom.stoer View Post
...3. but EPRL isn't correct; nevertheless a related Hamiltonian can exist, but it's not the correct one...
Just so we are clear what we mean (I suppose "EPRL" could mean different versions) could you make that specific to the spinfoam QG defined in the paragraph that I quoted? I'll bring it here and recopy.

If you can, please highlight where in the definition you believe it is not correct:
Let me now come to the main point of these lectures: the definition of the partition function of 4d Lorentzian LQG. This is defined by
ZC = Ʃjf,vef(2jf +1) ∏vAv(jf,ve), (67)
where C is a two-complex with faces f, edges e and vertices v, the intertwiners ve are in the space Ke = Kjf1 ...jfn where f1 , ..., fn are the faces meeting at the edge e and
Av(jf,ve) = Tr[⊗e∈v(fγve)]. (68)
where fγ is given in (54) and γ is a dimensionless parameter that characterizes the quantum theory, called Immirzi, or Barbero-Immirzi, parameter. This is the definition of the covariant dynamics of LQG.
Notice that the theory is entirely determined by the imbedding Yγ of SU(2) functions into SL(2,C) functions, defined in section IIIA, see equation (50). An intuitive track for understanding what is happening is the following. If we erase fγ in (68) we obtain the Ooguri quantization...
If it's inconvenient to point to something specific, perhaps you could say something more general about this particular formulation. I think all of us who've been taking part in the thread are familiar with this version, defined on page 13 of the Zakopane lectures of Loop gravity http://arxiv.org/abs/1102.3660.

I assume this is what you mean when you say "EPRL" and I'm curious to know what you think is incorrect about this particular version of Loop gravity.

My perspective on this is that we cannot know that it is incorrect. We have to devise ways to test by empirical observation so that nature can tell us if it is. It is normal for physical theories to turn out to be wrong, so one can speculate that this one (when confronted with data) will be shown to be wrong. But I don't see how you can say that in advance, at this point, with certainty.

Some elements of this definition may be contained in the earlier paper C. Rovelli and S. Speziale, Geometry of loop quantum gravity on a graph, Phys. Rev. D 82 044018
(2010), http://arxiv.org/abs/1005.2927. This is referred to by Freidel Geiller Ziprick 1110.4833. I'll check it out... No, that short paper is a precursor but it is too early, I think, to use as reference for the complete definition.
tom.stoer
#36
Feb5-12, 05:03 AM
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Quote Quote by marcus View Post
... and I'm curious to know what you think is incorrect about this particular version of Loop gravity.
To say that clearly: I don't simply say that the model is wrong; what I am saying is that the derivation of the model has some serious flaws (*), therefore I believe that the resulting model is physically wrong, i.e. has a dynamics which cannot be related to 'quantization of GR'. For some toy models where the correct quantization i.e. construction of H, PI and a map between them it is exactly known, one knows that repeating the flaws (*) leads to physically unacceptable PIs. This is a strong hint that EPRL is not correct.

Most of the problems are discussed in http://arxiv.org/abs/1112.1961v2
Some alternatives are discussed in http://arxiv.org/abs/1201.4247v1

If you ignore the construction and take EPRL as god-given, then there seems to be no problem; it's a consistent definition of model; the question why it should be the correct model is still open.


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