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Clear concise Loop survey as of January 2012

  1. Jan 24, 2012 #1

    marcus

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    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.
     
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  3. Jan 24, 2012 #2

    marcus

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    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.
     
  4. Jan 24, 2012 #3

    atyy

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    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?
     
  5. Jan 25, 2012 #4

    marcus

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    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."
     
    Last edited: Jan 25, 2012
  6. Jan 25, 2012 #5

    marcus

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    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.
     
  7. Jan 25, 2012 #6

    atyy

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    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).
     
  8. Jan 25, 2012 #7

    atyy

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    Yes, that's be helpful! One thing I don't understand is how spacetime can have a boundary - wouldn't that require AdS space?
     
  9. Jan 25, 2012 #8

    tom.stoer

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    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.
     
    Last edited: Jan 25, 2012
  10. Jan 25, 2012 #9

    marcus

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    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.
     
    Last edited: Jan 25, 2012
  11. Jan 25, 2012 #10

    marcus

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    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.
     
  12. Jan 25, 2012 #11

    atyy

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    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.
     
  13. Jan 31, 2012 #12

    marcus

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    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.
     
    Last edited: Jan 31, 2012
  14. Jan 31, 2012 #13
    In which paper, Barrett-Crane model's drawback was pointed out?
     
  15. Jan 31, 2012 #14

    marcus

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    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
     
  16. Jan 31, 2012 #15

    marcus

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    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.
     
    Last edited: Jan 31, 2012
  17. Jan 31, 2012 #16
    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.
     
  18. Jan 31, 2012 #17

    marcus

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    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..."
     
    Last edited: Jan 31, 2012
  19. Jan 31, 2012 #18

    marcus

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    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/First-Course-Loop-Quantum-Gravity/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!
     
    Last edited: Jan 31, 2012
  20. Jan 31, 2012 #19

    atyy

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    Thanks! I'll read it.

    Another introduction to the Thiemann Hamiltonian is
    http://arxiv.org/abs/1007.0402
    Introductory lectures to loop quantum gravity
    Pietro Doná, Simone Speziale
     
  21. Jan 31, 2012 #20

    marcus

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    Hey and that one is free online! (The textbook is rather pricey.) Good thought.
     
  22. Feb 1, 2012 #21

    tom.stoer

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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 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)
     
    Last edited: Feb 1, 2012
  23. Feb 1, 2012 #22

    marcus

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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==
     
    Last edited: Feb 1, 2012
  24. Feb 1, 2012 #23

    marcus

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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 :biggrin:

    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∈⊗⊕
     
    Last edited: Feb 1, 2012
  25. Feb 2, 2012 #24

    marcus

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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/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)
     
    Last edited: Feb 2, 2012
  26. Feb 2, 2012 #25

    marcus

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    Gold Member
    Dearly Missed

    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==
     
    Last edited: Feb 3, 2012
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