Clear concise Loop survey as of January 2012

[marcus]

Abhay Ashtekar has just posted a surehanded insightful survey of the main approaches to QG, focusing on current Loop hamiltonian and spinfoam developments. The first 8 or 9 pages give historical perspective. The next section gives a pedagogical introduction which will serve well the needs of newcomers. The last third is a perceptive account of what problems are currently driving Loop research and what potential developments he sees on the horizon. This last was especially interesting.

http://arxiv.org/abs/1201.4598
Introduction to Loop Quantum Gravity
Abhay Ashtekar
(Submitted on 22 Jan 2012)
This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad perspective on loop quantum gravity for young researchers. The first part is addressed to beginning students and the second to young researchers who are already working in quantum gravity.
30 pages, 2 figures.

 

[marcus]

Among many good points Ashtekar makes is this one where he removes a possible cause of misunderstanding by clarifying the incremental progress which is the goal of quantum relativity---not full unification but possibly a key step in that direction.
==quote page 13==
...as is the case with classical general relativity, while requirements of background independence and general covariance do restrict the form of interactions between gravity and matter fields and among matter fields themselves, the theory would not have a built-in principle which determines these interactions. Put differently, such a theory would not be a satisfactory candidate for unification of all known forces. However, just as general relativity has had powerful implications in spite of this limitation in the classical domain, quantum general relativity should have qualitatively new predictions, pushing further the existing frontiers of physics. Indeed, unification does not appear to be an essential criterion for usefulness of a theory even in other interactions. QCD, for example, is a powerful theory even though it does not unify strong interactions with electro-weak ones. Furthermore, the fact that we do not yet have a viable candidate for the grand unified theory does not make QCD any less useful.
==endquote==

I think it's clear that QG may turn out to be one of the steps along the road to a unified theory. But it is not itself a unification of forces. It aims to provide a quantum theory of geometry and matter without gettting into details about different matter species. Call it geometry-and-(generic)-matter if you like. Just as classic 1915 GR involves matter, so should the corresponding quantum theory.

 

[atyy]

I've always been unclear as to how the boundary state is chosen. It's interesting that he agrees a boundary state is the way to go, but that it's still not clear how to choose it (p25-26).

It's also interesting that he's considers linking up with string theory (p26). Wouldn't that indicate that the canonical programme shouldn't work since it's meant to be a pure gravity theory?

 

[marcus]

Just to be clear about it. GR is not a pure gravity theory. The right hand of the equation is matter, the left hand is geometry. It is about the relationship between geometry and matter.

quantum GR is not intended to be a pure gravity theory either.

But in developing QG one can certainly work on limited cases with very simple matter, or a restricted amount of matter etc. One of the more interesting ideas for this was described on pages 19-20 (Domagala et al).

Atyy I see no indication that he favors linking up with string, or believes that the theory needs it. What you refer to is a short passage on page 26 where he is speculating about future directions in research that MIGHT be explored. That is part of the job of a survey paper like this. He is laying out research possibilities to a broad audience of newcomers to the field and mentioning various things that might appeal to them.

The paper is short---only 27 pages plus references. He mentions a lot of different ideas for research. At the end of that short paragraph on page 26 he says http://arxiv.org/abs/1201.4598:
"string theory has two a priori elements: unexcited strings which carry no quantum numbers and a background space-time. Loop quantum gravity suggests that both could arise from the quantum state of geometry, peaked at Minkowski (or, de Sitter) space. The polymer-like quantum threads which must be woven to create the classical ground state geometries could be interpreted as unexcited strings. Excitations of these strings, in turn, may provide interesting matter couplings for loop quantum gravity."

 

[marcus]

I've always been unclear as to how the boundary state is chosen. It's interesting that he agrees a boundary state is the way to go, but that it's still not clear how to choose it (p25-26).

That's something we can try to figure out. In the paragraph you are talking about he is essentially disussing Rovelli's work on the graviton propagator, or 2-point function. That work was done around 2007. I will get a link. IIRC the spinfoam (representing the dynamics) was caged inside a fixed spin-network which had labels that determined the distances.
The spin network was the boundary state and allowed you to control the distance that the graviton was supposed to propagate. It was supposed to be attenuated by distance, according to inverse square.

 

[atyy]

GR is a pure gravity theory in the sense that the gravity degrees of freedom exist without matter, eg. the Schwarzshild solution. This was the initial point of view of canonical LQG. The contrasting viewpoint is unification, as tried by strings. So if loops and strings are related as Ashtekar speculates, then I don't think canonical LQG can work (or at least it's original philosophy wouldn't, maybe canonical LQG secretly contains matter).

 

[atyy]

That's something we can try to figure out. In the paragraph you are talking about he is essentially disussing Rovelli's work on the graviton propagator, or 2-point function. That work was done around 2007. I will get a link. IIRC the spinfoam (representing the dynamics) was caged inside a fixed spin-network which had labels that determined the distances.
The spin network was the boundary state and allowed you to control the distance that the graviton was supposed to propagate. It was supposed to be attenuated by distance, according to inverse square.

Yes, that's be helpful! One thing I don't understand is how spacetime can have a boundary - wouldn't that require AdS space?

 

[tom.stoer]

There are two main issues with LQG as of today:
- incomplete understanding of quantization including dynamics (Hamiltonian, constraints, consistency, LQG and SF models)
- coupling to matter and renormalization

The first point is rather technical so I think it's clear why Ashtekar does not discuss these topics; the second is of major relevance due to the asymptotic safety program and the question of non-Gaussian fixed points when matter is coupled to gravity.

 

[marcus]

I've always been unclear as to how the boundary state is chosen. It's interesting that he agrees a boundary state is the way to go, but that it's still not clear how to choose it (p25-26).

That's something we can try to figure out. In the paragraph you are talking about he is essentially disussing Rovelli's work on the graviton propagator, or 2-point function. That work was done around 2005-2008. I will get a link. IIRC the spinfoam (representing the dynamics) was caged inside a fixed spin-network which had labels that determined its proportions.
The spin network was the boundary state and allowed you to control the distance that the graviton was supposed to propagate. It was supposed to be attenuated by distance, according to inverse square.

The germ of the idea of using a fixed boundary state is in the 2005 paper. Beginning this far back may make it easier to understand because the earlier exposition spells it out in more detail.
http://arxiv.org/abs/gr-qc/0508124
Look on page 3
The boundary state cage is just going to be the spin network bounding a 4 simplex!
The spinfoam is just inside the 4 simplex itself. Everything is reduced to simplest form.
It's going to get more complicated in the next paper but for now it's extremely rudimentary.

At the top of page 3:
"... The sums over permutations in the propagator give rises to a number of terms. Each of these can be interpreted as a spinfoam σ, by identifying closed sequences of contracted deltas as faces. Hence the amplitude.. can be written as a sum of amplitudes of spinfoams bounded by a given spinnetwork W... an expression that is naturally interpreted (and can also be derived) as a sum over discretized 4-geometries bounded by a given discretized 3-geometry, namely as a definition of the Misner-Hawking sum-over-geometries formulation of quantum gravity, ..."

I think that was the first graviton propagator paper---then there were a series 2006-2008 which eventually led to the replacement of the Barrett-Crane model by the EPRL.

The next paper was 2006 http://arxiv.org/abs/gr-qc/0604044
see Figures 1, 2, 3...,6 on pages 26-30

By that time as you can see they are already using more complicated boundaries enclosing more complicated foams. But the germ of the idea was already in Rovelli's 2005 paper.

The process did not stop until they had discovered there was trouble with the Barrett-Crane foam and replaced it (by around 2009)---then the dust kind of settled on that and there was the new formulation of LQG in 2010 and 2011. You could say that the conclusion of that arc of transition was the Zakopane Lectures
http://arxiv.org/abs/1102.3660.

When Ashtekar talks about "boundary state" he is acknowledging all that. The work on the graviton propagator was really critical. But now I think the field is ready for another unpredictable move. Ashtekar's paper should be a good one to study while trying to imagine what that could be.

 

[marcus]

Yes, that's be helpful! One thing I don't understand is how spacetime can have a boundary - wouldn't that require AdS space?

The boundary is what divides the quantum experiment from the guy in the white coat.

It defines a finite region of spacetime, whose geometry we are going to study.

When Rovelli uses the "boundary formalism" he is not suggesting that the whole of the universe has a boundary.

You can think of what the box encloses as approximately Minkowski space---not even as fancy as deSitter or anti-dS. The whole idea was to be able to derive an inverse square law.

The boundary here is somewhat analogous to the box in which Schroedinger cat sits. It helps to define what the external experimenter can measure and observe. The boundary helps to distinguish between the quantum system being studied and the (classical?) world of the observer outside. Philosophically that's what it represents I think.

 

[atyy]

The boundary is what divides the quantum experiment from the guy in the white coat.

It defines a finite region of spacetime, whose geometry we are going to study.

When Rovelli uses the "boundary formalism" he is not suggesting that the whole of the universe has a boundary.

You can think of what the box encloses as approximately Minkowski space---not even as fancy as deSitter or anti-dS. The whole idea was to be able to derive an inverse square law.

The boundary here is somewhat analogous to the box in which Schroedinger cat sits. It helps to define what the external experimenter can measure and observe. The boundary helps to distinguish between the quantum system being studied and the (classical?) world of the observer outside. Philosophically that's what it represents I think.

I understand it as a low energy approximation - maybe like what Giddings discusses in http://arxiv.org/abs/1105.2036. But if I recall from Rovelli's http://arxiv.org/abs/1102.3660, it seems that the whole spin foam framework requires this boundary to calculate anything - how can that be the case for cosmology - ie. outside a particle physics experiment? I suppose I should see how Vidotto approaches this.

 

[marcus]

But if I recall from Rovelli's http://arxiv.org/abs/1102.3660, it seems that the whole spin foam framework requires this boundary to calculate anything - how can that be the case for cosmology...

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.

I'll get a page reference. You can see from the Table of Contents that it is mostly about HAMILTONIAN approach but the last section, section IV, gets into spinfoam cosmology:
IV. Spinfoam Dynamics 23
A. The Spinfoam Cosmology Setting 23
B. Spinfoam Amplitude and Dynamics for BF Spinfoam 26
C. Asymptotic Behavior and FRW Equation 28
D. Recovering the Hamiltonian Constraint 29
E. How to Depart from Flat Cosmology? 31
F. Cosmological Dynamics with Holomorphic Simplicity Constraints 32

Here is an excerpt from page 25:
==quote==
4. The Group Field Theory Point of View and the Issue of Renormalization
Here, we have taken the point of view of fixing both the boundary graph Γ on which our spin networks live and the bulk spinfoam 2-complex ∆. Our goal is to compute the corresponding spinfoam amplitudes describing the evolution and dynamics of the spin networks for this fixed choice of bulk structure and interpret as a mini-superspace model (for cosmology).
An alternative would be to fix the structure of the boundary but sum over all “admissible” bulks. In order to do this, we need to define the list of admissible 2-complexes and to fix their relative weights in the sum. This is done automatically by the group field theory formalism which provides us with a non-perturbative definition of the sum over spinfoam histories for fixed boundaries (see e.g. [32, 33]).
==endquote==

Incidental BTW http://www.iem.csic.es/departamentos/qft/CV/CV_Martin-Benito.html
I'm just guessing Meché as a nickname for Mercedes. A friend in Bogota Colombia goes by Mechás
but I think Meché is more common.

 

[Karmerlo]

In which paper, Barrett-Crane model's drawback was pointed out?

 

[marcus]

In which paper, Barrett-Crane model's drawback was pointed out?

It was a 2007 paper by Rovelli and Alesci. I'll look it up.
http://arxiv.org/abs/0708.0883
The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex

 

[marcus]

That reminds me! I'd like to find a good way for a new person 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.

In at least one case a proposal has been worked out in 3D but not in 4D. In at least one other case only an idea has been presented.

I would like to get other people's ideas. Some may think that LQG has a definite hamiltonian (they may disagree with me.)

First, I can give some indication of the unsettled situation by linking to some technical papers but this is definitely NOT A GOOD INTRODUCTION because exploratory proposals are the complete opposite from textbook-expository style introductions. So these are just things to have heard of and realize how much in flux the situation is. Just to have heard of, not even to know anything definite about.

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). Also I just noticed that Valentin Bonzom, a young postdoc researcher, shows up in two of the three cases.

 

[Karmerlo]

It was a 2007 paper by Rovelli and Alesci. I'll look it up.
http://arxiv.org/abs/0708.0883
The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex

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.

 

[marcus]

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.

By coincidence I just started responding to that question a few minutes ago in the preceding post! Your question reminded me! Here is what I had written so far:
==quote post #15==
...I'd like to find a good way for a new person 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.

In at least one case a proposal has been worked out in 3D but not in 4D. In at least one other case only an idea has been presented.

I would like to get other people's ideas. Some may think that LQG has a definite hamiltonian (they may disagree with me.)

First, I can give some indication of the unsettled situation by linking to some technical papers but this is definitely NOT A GOOD INTRODUCTION because exploratory proposals are the complete opposite from textbook-expository style introductions. So these are just things to have heard of and realize how much in flux the situation is. Just to have heard of, not even to know anything definite about.

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). Also I just noticed that Valentin Bonzom, a young postdoc researcher, shows up in two of the three cases.
==endquote==
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..."

 

[marcus]

I see that in this list of 4 papers proposing Hamiltonians for LQG Livine and Bonzom both appear twice. So they are people to watch as we look for the establishment of a satisfactory Loop Hamiltonian, and also likewise are Freidel, Rovelli, Alesci, Oriti, and Ryan.

It's pretty exciting. Starting around 2009 or 2010 Loop research began a period of rapid development. Much of what people are dealing with is of fairly recent origin.

To respond to your question, which was specifically about INTRODUCTORY material. I would say this

1. One way into the subject is through Loop cosmology. That is a radically simplified version of LQG. It has a definite Hamiltonian. It says stuff about the beginning of expansion. The universe is much simpler than the general theory because it looks like on average constant curvature and there is a "universe time" that cosmologists use.
The main authority in the application to cosmology is Abhay Ashtekar so you can just browse his papers on arxiv until you find something suitable.
He has one called "Introduction to LQG through cosmology." He has a recent pedagogical review of straight LQG which is the topic of this thread.

2. Since the Hamiltonian approach to LQG is still unsettled and not yet ripe for an introductory presentation IMHO, another way to get into the subject is to learn the spinfoam approach. For example http://arxiv.org/abs/1102.3660. If that is not suitable, there are more introductory treatments, I could try to help dig up some.

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.
https://www.amazon.com/dp/0199590753/?tag=pfamazon01-20
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!

 

[atyy]

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.

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.

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.
https://www.amazon.com/dp/0199590753/?tag=pfamazon01-20
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]

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]

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 https://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]

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 f_γ 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]

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
Z_C = Ʃ_jf,ve ∏_f(2j_f +1) ∏_vA_v(j_f,v_e), (67)
where C is a two-complex with faces f, edges e and vertices v, the intertwiners v_e are in the space K_e = K_{jf1 ...jfn} where f1 , ..., fn are the faces meeting at the edge e and
A_v(j_f,v_e) = Tr[⊗_e∈v(f_γv_e)]. (68)
where f_γ 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 Y_γ 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 f_γ 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:
https://www.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/au:+Madore_J/0/1/0/all/0/1


ινξςυφΓΘΛΞΠΣΦΨ⋅∗ℤℕ∈⊗⊕

 

[marcus]

I want to see how this paper fits into 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/au:+Freidel_L/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]

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]

... 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]

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.

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 f_γ 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 Y_γ 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]

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 definately 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]

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...

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 f_γ, 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]

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]

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]

@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]

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:

@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]

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]

...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
Z_C = Ʃ_jf,ve ∏_f(2j_f +1) ∏_vA_v(j_f,v_e), (67)
where C is a two-complex with faces f, edges e and vertices v, the intertwiners v_e are in the space K_e = K_{jf1 ...jfn} where f1 , ..., fn are the faces meeting at the edge e and
A_v(j_f,v_e) = Tr[⊗_e∈v(f_γv_e)]. (68)
where f_γ 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 Y_γ 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 f_γ 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]

... 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.

 

[atyy]

What exactly is the problem with Thiemann's constraint? Is it inconsistent? Or is it consistent but not known to give the Einstein equations in the classical limit?

 

[tom.stoer]

Do you mean Thiemann's "old approach" or his new work?

Regarding the old approach it is clear that the action of H on physical states creates only trivial new vertices carrying zero volume. This ensures consistency of the constraint algebra but is physically not acceptable.

Regarding the new papers I have to admit that I haven't studied them in detail, unfortunately.

 

[atyy]

Yes, his old work.

Is the old Thiemann constraint unphysical because it doesn't implement the Dirac quantization? Or is it possible to implement the Dirac quatization and still be unphysical?

 

[tom.stoer]

The old constraint does not obiously violate the Dirac quantization; the algebra closes, but non-trivially, i.e. commutators of constraints are linear combinations of constraints but with "constraint dependent structure functions"; that means that operator ordering and regularization will become ambiguous.

The first problem is the step-by-step approach to constraint implementation. Usually you have a set of first class constraints, you quantize and regularize them and then you implement them (all at once) as constraints on physical states. Doing it that way guarantuees that you can check the consistency of the regularization and operator ordering with the constraint algebar in each step.

Doing it like Thiemann et al. in a stepwise approach first all constraints but H go away leading to the kinematical Hilbert space of spin networks; what remains is H. The linear combinations of constraints with constraint dependent structure functions calls for a deeper understanding; one may worry that the regularization and operator ordering of H is inconsistent, but this inconsistency doesn't show up on-shell in the kinematical Hilbert space; in addition there is no control on the off-shell closure of the constraint algebra b/c the other constraints have been implemented already.

So the first problem is that inconsistencies in H cannot be checked against the symmetries of the theory. I do not know whether Thiemann's master constraint approach has changed this in a fundamental manner.

The second problem is that the last constraint to be implemented is H; when you regularize it a la Thiemann you find that its quantum version suffers from being unphysical; of course one may suspect that it is related to the first problem.

The general problem is that there are many different inequivalent constructions of H, all of them can be motivated somehow (Rovelli found one that 'creates volume' and therefore could be physically acceptable), but all suffer from the stepwise approach (all of them act in the same kinematical Hilbert space) which means that the first problem is never addressed.

I do not even know if there is consensus whether the first problem is a problem at all. It's like the EPRL model: you have something that has some strange features (physically) and a rather weird construction (mathematically). Therefore you may suspect that both are related, but the theory doesn't provide tools via which you can double-check.

 

[atyy]

Ok, I'm confused - Thiemann's old approach isn't his master constraint?

 

[marcus]

To say that clearly: I don't simply say that the model is wrong; what I am saying is that the derivation...

Thanks for the reply. The Zako spinfoam QG theory whose definition I just now quoted is not derived. As I recall this point was made explicitly up front in the Lectures. Maybe we should carefully distinguish between this and the pre-2010 EPRL.

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

But neither paper addresses the Zako spinfoam QG theory I was talking about. I can only find citation to previous EPRL and stuff like that. It does not seem relevant.

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.​

I assume that by "construction" you mean derivation. But the theory I'm asking you about is not derived. It has no derivation. So there is no "construction" to be ignored. Of course like any man-made theory it has a mathematical construction (basically due to Eugenio B, or completed by him, it is said) and it's a rather nice one I think. But that comes under the "consistent definition" you talk about.

I am not sure what exactly you mean when you say EPRL, since the references you give never seem to cite or discuss the spinfoam theory I am asking you about.

Maybe we should use a different abbreviation for post-2010 spinfoam as in Zakopane Lectures---from which I quoted the definition in post #35. Should we say ZQG?
Or ZLQG? Z for Zakopane.

I'm really interested in your thoughts and impressions about ZQG, not about EPRL. Like e.g. the fact that there is nothing in the model called "simplicity conditions" (but surely the same effect must essentially be achieved by a different route. Or no?)

That's an interesting question and I wonder what your take on it is. Is the effect of the pre-2010 EPRL "simplicity" requirement achieved in ZQG even though not imposed as such?
========================
For handy reference I'll copy your full post:

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.

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

BTW one nice thing about Ashtekar's historical/overview survey here is that it was the opening talk at Zakopane and will serve as the introductory chapter of the book of Proceedings. So among other things, Ashtekar's intro repeatedly refers to Rovelli's Z Lectures which are to be bound in the same volume, as well as to chapters/talks by others at the Zakopane QG school. Whenever Ashtekar is talking about spinfoam he naturally refers to the ("ZQG") chapter by Rovelli. So Ashtekar is pointing the reader at what I'm called ZQG to distinguish it from earlier spinfoam models often called EPRL.
I hope they do go ahead and, as Ashtekar indicates, prepare a bound volume of proceedings. It could turn out to be a useful book.

BTW this talk Eugenio gave in January 2010 at Sophia-Antipolis may help clarify the history or make the connections. The f_γ notation appears around slides 23, 24. But it seems not yet to denote quite what it came to stand for later that year: a mapping from FUNCTIONS on SU(2) to functions on SL(2,C).
http://wwnpqft.inln.cnrs.fr/pdf/Bianchi.pdf

 

[tom.stoer]

The Zako spinfoam QG theory whose definition I just now quoted is not derived. As I recall this point was made explicitly up front in the Lectures.

Yes, Rovelli was rather clear about that point, but of course he is wrong ;-)
- his model is not derived in all details, but inspired in many ways by several related derivations
- I strongly believe that the steps where a derivation is missing are the most problematic ones

Maybe we should carefully distinguish between this and the pre-2010 EPRL.

Perhaps I miss something, so let me ask you: what is the major difference between the "pre2010 EPRL" and the Zako-EPRL? My impression always was that Zako-EPRL does not address the fundamental issues of EPRL (and FK).

But the theory I'm asking you about is not derived. It has no derivation.

As I said: I don't think that there is not any (partial) derivation; and I don't think that the missing (complete) derivation is a benefit - it's a drawback.

I'm really interested in your thoughts and impressions about ZQG, not about EPRL. Like e.g. the fact that there is nothing in the model called "simplicity conditions"

w/o derivation that's difficult to say b/c the simplicity constraints would show up in delta functions and the PI measure.

 

[marcus]

- his model is not derived in all details, but inspired in many ways by several related derivations
- I strongly believe that the steps where a derivation is missing are the most problematic ones​

As he says, it is inspired by several derivations.
There are no isolated "steps" or "details" apart from which it is derived.

Perhaps I miss something, so let me ask you: what is the major difference between the "pre2010 EPRL" and the Zako-EPRL? My impression always was that Zako-EPRL does not address the fundamental issues of EPRL (and FK).
​

No explicit equation called "simplicity constraint" is needed. That is a big difference. In an earlier post I already called your attention to the f_γ mapping from functions on SU(2) to functions on SL(2,C).

 

[tom.stoer]

marcus, please have a careful look at Rovelli's paper:

http://arxiv.org/abs/1102.3660
Zakopane lectures on loop gravity

On page 3 he presents the definiton for Z (eq. 3); then he writes

"The expression (3) was found independently and developed
during the last few years by a number of research
groups [15-21], using dierent path and different
formalisms (and a variety of notations). Different definitions
have later been recognized to be equivalent. The
resulting theory is variously denoted as EPRL model,
EPRL-FK model, EPRL-FK-KKL model, new BC
model ... in the literature. I call it here simply the partition
function of LQG. The presentation I give below does
not follow any of the original derivations."

So based on this I can't see anything that is new compared to

[15] arXiv:gr-qc/9709028.
[16] arXiv:0705.2388.
[17] arXiv:0705.0674.
[18] arXiv:0708.1236.
[19] arXiv:0708.1595.
[20] arXiv:0711.0146.
[21] arXiv:0909.0939.

On page 14 he writes

"general relativity is BF theory plus the simplicity constraints."

So again he stresses the importance of these auxiliary condition introduced by hand to break the symmetry of the topological BF theory.

In (135) he explicitly introduces the constraint K+γL=0 and refers to its kernel or "subspace".

You will see that (135) is core to the whole construction, but that compatibility of constraints, second-class constraints etc. are never discussed. So this Zako-EPRL has the same weak-points as all prior references [15-21].

Regarding his map f_γ: I don't see how this map changes the situation for consistency of (135). On page 14 he writes

"The map f_γ implements the simplicity
conditions, since it maps the states to the space where
the simplicity conditions (51) hold;"

This is true w/o doubt.

The problem is not the implementation of (51) itself, but the consistency of (135) with other constraints. This issue is simply not discussed, nowhere!

It should be clear that adding a new constraint changes the symplectic structure of the theory. Studying the the algebra of (135) with other constraints (G,D and H) one finds that (135) is second class and must be implemented a la Dirac which explicitly changes the symplectic structure. Rovellis et al. ignore this procedure completely, they quantize the unmodified symplectic structure of the BF theory instead, and impose (135) after quantization.

So basically what is wrong with the EPRL model (in all its variants) is the following: in the presence of second-class constraints we know from Dirac that one must first solve the second-class constraints consistently in the classical phase space and then quantize the system on the reduced phase space.

Dirac:
(1) derive or introduce all constraints
(2) calculate the Dirac brackets or solve second class constraints explicitly
(3) quantize

'Babel':
(1) derive some constraints
(2) calculate the Poisson brackets
(3) quantize
(4) introduce new constraints

For all models where one can solve the theory explicitly it is known that 'Babel' is wrong, whereas 'Dirac' is right (in the physical sense); unfortunately the quantization procedure of EPRL corresponds to 'Babel'! Here 'wrong' referes to a wide range of possibilities; there can be quantization anomalies which render the resutung quantum theory inconsistent - or it can simply mean that 'Dirac' and 'Babel' result in physically different theory with different dynamics, different degrees of freedom etc. In a situation w/o any good foundation for a different (consistent) constraint quantization procedure but Dirac (EPRL never mentions something like that) I am still with Dirac.

 

[marcus]

The last section of Zako Lectures before the "conclusions" is a 4-page "Section V" which could be called "Several Heuristic Not-Quite Derivations".
It's included for didactic, motivational purposes and for historical continuity. The theory is presented NOT as derived and none of the derivations from other areas of theory reaches it although I would say they converge towards it.

This is explained clearly at the start of Section V in a warning not to treat these (quasi-)derivations as if they presented as a way of straightforwardly deriving the QG theory itself as formulated earlier.

(But see Tom's post #45 where he makes repeated references to equation 135 and other stuff from this 4-page section at the end.)

But this historical heuristic discussion is, I think, quite interesting! Section V starts at the bottom of page 23 and it has 4 parts
A. Dynamics (quantization from BF theory using a simplicity constraint, see eqn. 135)
B. Kinematics (mentions that we don't yet have a conjoined hamiltonian approach)
C. Covariant lattice quantization (yet another quasi-derivation, explains how eqn. 135 can be viewed as a reality condition.)
D. Polyhedral quantum geometry (interesting new approach to formulating the theory)

 

[marcus]

Ashtekar's Loop survey was the opening talk at the Zakopane QG school which was predominantly about the post-2010 (not derived) formulation of Loop gravity which I've sometimes called ZQG to distinguish it from pre-2010 "EPRL" and such, that many people seem very attached to.

This version of Loop gravity is clear and can be presented definitively in a couple of pages. The essentials in a single paragraph, as I quoted.

Google "Rovelli Zakopane" and you get http://arxiv.org/abs/1102.3660, see page 13.

So what's the outcome of this development? Where is the community going from here?

One very interesting new development, I think, is that Laurent Freidel with the help of some smart new people has begun to develop LOOP CLASSICAL GRAVITY. You can see this as a reaction to ZQG, even as in a sense taking off from Zakopane as a point of departure.

I urge anyone at all interested in QG to watch at least the first 28 minutes of Jon Ziprick's recent PIRSA video.

Google "Ziprick PIRSA" and you get http://pirsa.org/12020096. The last 35 minutes is Lee Smolin and Laurent Freidel and Bianca Dittrich (who is great) arguing about what Ziprick said in the first 28 minutes. Do watch at least the first part!

Here's what I think is the essential. Relativity has infinite degrees of freedom. What if we use the partial ordering of graphs to truncate GR to a partial ordered crowd of finite DoF theories, and then get continuum GR as a projective limit?

The finite DoF version of GR, based on a graph, is still classical. Suggestively, we can call it Loop Classical Gravity. Or loop classical geometry if you like that better. LCG anyway.

Then it will be straightforward to quantize LCG and so to actually derive LQG. In essence that is the plan, as I see it.

Eugenio Bianchi is also involved in that intense discussion following Ziprick's presentation (of the Loop Classical Gravity approach) around minute 49. Bianca comes in around minute 37 and again around minute 50. There is someone sitting next to her, guy in a red shirt I don't recognize. He joins the discussion around minute 45. Laurent talks a lot, it is a serious discussion with quite provocative ideas.

 

[atyy]

Here's what I think is the essential. Relativity has infinite degrees of freedom. What if we use the partial ordering of graphs to truncate GR to a partial ordered crowd of finite DoF theories, and then get continuum GR as a projective limit?

What, what? Really? That is the anti-Rovelli view - his Zakopane lectures clearly do not take this approach. It seems very much like a Dittrich view. I'll definitely watch the video when I have time, sounds great. In the Rovelli view, there should be a continuum "upwards", which you can also get by going "downwards" see the figure on p21 of the Zakopane lectures. Dittrich has for quite some time been contemplating that you can only get the continuum by going "downwards". (Well, to be fair, she's also contemplated the relationship to Asymptotic Safety, which is a continuum "upwards" philosophy.)

Why does Rovelli want the "upwards" limit to also hold? I think this is because he wants to get the full match to the canonical LQG states. I think the only sense in which the Zakopane lectures go beyond EPRL is that they incorporate KKL's generalization to get a full match to canonical LQG states. In this sense, I think tom.stoer is right that Rovelli is still quite concerned with the relationship between canonical LQG and EPRL.

Other places in the Zakopane lectures that emphasize the continuum upwards, and KKL's extension of EPRL are:
p14: "The resulting expression naturally generalized to an arbitrary number of nodes and vertices, and therefore defines the dynamics in full LQG. The existence of this generalization was emphasized in [21]."
p21: "The theory is given by the formal limit of infinite refinement for transition amplitudes defined on finite two complexes. But we may not need to take the limit to extract approximate predictions from the theory.²¹"

So the Zakopane lectures are really about EPRL, or more properly EPRL-FK-KKL, which is a term Rovelli mentions on p3.

 

[marcus]

In this sense, I think tom.stoer is right that Rovelli is still quite concerned with the relationship between canonical LQG and EPRL.

Of course he is concerned with the relation between (as yet not formulated) canonical and the spinfoam formulation! You can see that in the recent Alesci Rovelli proposal for a Hamiltonian that (finally) can increase volume! One that uses tets rather than triangles. No one has said not concerned.

My point is about the correctness of the Zakopane "ZQG" spinfoam formulation, which is explicitly presented as not derived by quantization (and the reasons for this are clearly explained). No one can truthfully say that a physical theory that is clearly predictively formulated like that is not correct until it has been tested. We do not know the future. It is consistent with past observation as far as we know.

So the Zakopane lectures are really about EPRL, or more properly EPRL-FK-KKL, which is a term Rovelli mentions on p3.

What they are "really about" is a matter of individual interpretation. They mainly feature the new "ZQG" formulation which is superior in many ways to the pre-2010 "EPRL-FK-KKL".
But of course when you make a new formulation, one that is far more concise, you want to go back and show the connections and the historical continuity. So if you like you can say that any new formulation is "really about" the antecedents and motivation that gave rise to it.
=======================
It is superstition to believe that a new physical theory is not correct unless it is derived by some established procedure from past theory which has been successful in the past. At times physics has advanced by a smart/lucky guess, or in other ways.

The big thing that I am looking for now are the repercussions. The reaction by Laurent Freidel, for example. If possible he will try to show that Rovelli's message about "probably no straightforward derivation from GR is possible" to be wrong.
There is always a Hegelish dialectic of thesis-antithesis-synthesis going on.
Now Freidel will study how you "really" should quantize GR, by first FINITIZING it into a kind of "Loop Classical Gravity" based on finite graph states of geometry. And then the finite LCG will be quantizable in a straightforward way.

And in the process this will again transform Loop gravity. It could even nullify it (according to Jon Ziprick) if one can show that it is impossible to finitize classical GR with finite graph-based (holonomyflux) dynamics. This comes out around minute 27-28 of the talk and sets off the serious discussion by Smolin Freidel Dittrich Bianchi and the guy in the red shirt with the french? accent.

Rovelli's conjecture is plausible enough, and Freidel will work hard to show it wrong or partially wrong and partially right in the sense I have described. It is plausible because no straight quantization of GR has appeared in over 60 years of trying. If there were one it probably would have appeared. And it has happened in physics in the past that sometimes one has to make a guess and formulate something in a radically new way. It is plausible, then, but not necessarily right. We have to see.
===================

For newcomers who want to look at what is being discussed:

Google "rovelli zakopane" and get http://arxiv.org/abs/1102.3660
Google "ashtekar introduction 2012" and get http://arxiv.org/pdf/1201.4598.pdf
Google "jonathan ziprick pirsa" and get the video http://pirsa.org/12020096 - Continuous Formulation of the Loop Quantum Gravity Phase Space--watch first 28 minutes

 

[atyy]

It is superstition to believe that a new physical theory is not correct unless it is derived by some established procedure from past theory which has been successful in the past. At times physics has advanced by a smart/lucky guess, or in other ways.

Yes, of course. I was actually trying to be as uninterpretive in what I wrote. My interpretation is that Rovelli is still too close to canonical LQG in trying to interpret EPRL.