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A new spinfoam vertex probably MIP for second quarter

  1. May 8, 2007 #1

    marcus

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    "A new spinfoam vertex" probably MIP for second quarter

    The new paper of Livine and Speziale could very well turn out to be the most influential paper of second quarter 2007.
    http://arxiv.org/abs/0705.0674
    A new spinfoam vertex for quantum gravity

    A large part (perhaps majority) of research effort in non-string QG is focused on the spinfoam approach.

    this is a path integral, or sum-over-histories approach-----the spinfoam is a 4D spacetime path linking two spinnetwork quantum states of geometry, a "before" state and an "after" state.

    Each spinfoam is a way that one state can evolve into another, and for each such spinfoam "evolutionary pathway" it must be possible to compute an AMPLITUDE. One should be able to sum or average-----to integrate over all these spinfoams---to get the overall amplitude of one particular state evolving into another.

    the amplitude of a spinfoam is computed by evaluating a vertex function of the data at each vertex. Also every spinfoam has a dual where each 4D simplex is replaced by a vertex and vice versa, do I suppose one can think of the vertex function being evaluated on each simplex of the dual: block by block.

    until now much of the spinfoam research effort has focused on the BARRETT-CRANE model, where one uses a particular BC vertex function.
    The BC model has attractive features---as explained in this paper, among others---but also one or more drawbacks, which Livine and Speziale mention as well.

    It seems to me that what Livine and Speziale are proposing to do is break a potential log-jam in spinfoam research by offering a NEW vertex function---call it the "LS model" or the "LS vertex"---which will not have these drawbacks.

    Two reasons I like their paper are (1) it is clearly written (they put care into making it understandable) and (2) they have been doing numerical work---such as computer simulations---in parallel with their theoretical progress. Each theory step they take, they try it out and support it with numerical work.
     
    Last edited: May 8, 2007
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  3. May 8, 2007 #2

    marcus

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    the two other papers that I think are in the running for second quarter MIP are one by Bojowald and one by Rovelli et al.

    http://arxiv.org/abs/gr-qc/0703144
    Dynamical coherent states and physical solutions of quantum cosmological bounces
    Martin Bojowald
    30 pages, 3 figures

    "A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce."
    (the Bojowald paper appeared right at the end of March and was not included in our first quarter poll)

    http://arxiv.org/abs/0705.0006
    Multiple-event probability in general-relativistic quantum mechanics: a discrete model
    Mauricio Mondragon, Alejandro Perez, Carlo Rovelli

    "We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally-covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper. We consider a version of the model with unitary time-evolution and a version without unitary time-evolution."

    Also there are almost 8 more weeks left to the quarter, which is April-June. So that is what the competition looks like for the Livine/Speziale paper. Here is the abstract:

    http://arxiv.org/abs/0705.0674
    A new spinfoam vertex for quantum gravity
    Etera R. Livine, Simone Speziale
    25 pages 6 figures

    "We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints."

    (Submitted on 4 May 2007)

    To get a better idea of the possible significance of the Livine-Speziale spinfoam, I will exerpt the first paragraph of their introduction:

    "The spinfoam formalism for loop quantum gravity (LQG) [1] is a covariant approach to
    the definition of the dynamics of quantum General Relativity (GR). It provides transition
    amplitudes between spin network states. The most studied example in the literature is the
    Barrett–Crane (BC) model [2]. This model has interesting aspects, such as the inclusion
    of Regge calculus in a precise way, but it can not be considered a complete proposal. In
    particular, recent developments on the semiclassical limit show that it does not give the
    full correct dynamics for the free graviton propagator [3]. In this paper we introduce a
    new model that can be taken as the starting point for the definition of a better behaved
    dynamics.
    "
     
    Last edited: May 8, 2007
  4. May 8, 2007 #3

    marcus

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    How to see these papers, and judge their importance, in what context? In what perspective?

    By coincidence the clearest short perspective on non-string QG that I can remember hearing anytime recently was what f-h wrote in another thread here at PF.
    https://www.physicsforums.com/showpost.php?p=1319163&postcount=38
    https://www.physicsforums.com/showthread.php?p=1319163#post1319163

    ==exerpt from f-h post==
    "...LQG as used here is not a theory it's a conglomerate of vaguely related or philosophically sympathetic theories. The original LQG ideas are today mostly pursued by Thiemann, most everyone else has moved and tried different ideas and theories.

    You are also ignoring the fact that LQG was pursued for ten years by a very small number of people, and that new results (not revolutions, incremental results) chipping away at the problems have been and are coming.

    The complexity of String Theory seems to me to be purely mathematical, compared to that, the approaches pursued in the LQG community are varied and physically/philosophically much more sophisticated.

    You say that the majority of QG people are convinced that by searching these mathematical complexities they will eventually (incidentally?) arrive at the physical subtleties. Correct? But is there any evidence of that?

    And that is an appealing thing in LQG, and the reason I chose to study it. If you look at the things Carlo Rovelli for example has worked on, these insights (relational formulations, local particle concepts, etc.) will by neccesity play a role in the final theory. They arise out of a straightforward combination of GR and QM!

    Much of the LQG type research is pursued in this spirit. So in fact the time spans have been much shorter.
    And it is this spirit that I think Smolin is asking for. Instead of looking for physics in the mathematical complications of one particular approach, as fascinating as they may be, it might be prudent to look at other approaches to do physics. Or at least acknowledge them..."
    ==endquote==

    I think the key phrase here is chipping away at the problems-----and this process informed by a philosophical vision like a sculptor who can "see" into the rock to what features the final piece must have.

    Each of the three papers mentioned here represents incremental progress or at least the possibility of it.
    Bojowald has been resolving the cosmological singularity step by step since 2001, always enlarging the solution to encompass more and more generality.
    Now, at this stage, he presents an exactly solvable LQC model which can serve as anchor for a perturbative treatment of a more general LQG bounce.

    Rovelli, as he often has done in the past, has identified a problem which must be addressed, whatever the ultimate shape taken by background independent QG. So he and his fellow authors focus this in a simplified case where only this one problem is conspicuous---as he has done in past with relational time, relational observables, the problematical concept of "particle", etc.

    The Livine Speziale paper is slightly more of a leap, I think. It is still incremental in the sense that there has been a lot of work by them and many others on the BC spinfoam and what they have done here is identify a way to fix a problem with the BC spinfoam*, which still retains the good properties of the BC model. But it is a big project to check that the LS model works as expected. So we may not be able to get a very good idea right away of how LS spinfoam is working out.

    Maybe by late June, when we set up the "Most Influential Paper" forecast poll there will be more to go on.

    *read post #2 in this thread, where the quoted passage from L-S introduction describes this, with appropriate qualifications. I am paraphrasing from the previous post.
     
    Last edited: May 8, 2007
  5. May 8, 2007 #4
    What problem is that and how do they propose to fix it?
     
  6. May 9, 2007 #5

    marcus

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    the second quarter of 2007 is not even half over and already we have FOUR clear candidates for paper most valuable to future research in non-string QG.
    A new one showed up today, by Giddings and Marolf. So here is the list so far:

    http://arxiv.org/abs/gr-qc/0703144
    Dynamical coherent states and physical solutions of quantum cosmological bounces
    Martin Bojowald
    30 pages, 3 figures

    "A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. ... an exactly solvable model ... basis for a systematic perturbation theory of loop quantum gravity... remarkably different from what is known for harmonic oscillator coherent states. ... the quantum state ... evolve deterministically through the bounce."


    http://arxiv.org/abs/0705.0006
    Multiple-event probability in general-relativistic quantum mechanics: a discrete model
    Mauricio Mondragon, Alejandro Perez, Carlo Rovelli

    http://arxiv.org/abs/0705.0674
    A new spinfoam vertex for quantum gravity
    Etera R. Livine, Simone Speziale
    25 pages 6 figures

    "We introduce a new spinfoam vertex to be used in models of 4d quantum gravity ... We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations..."

    "The spinfoam formalism for loop quantum gravity (LQG) [1] is a covariant approach to the definition of the dynamics of quantum General Relativity (GR). It provides transition amplitudes between spin network states. The most studied example in the literature is the Barrett–Crane (BC) model [2]. This model has interesting aspects, such as the inclusion of Regge calculus in a precise way, but it can not be considered a complete proposal. In particular, recent developments on the semiclassical limit show that [the older BC model] does not give the full correct dynamics for the free graviton propagator [3]. In this paper we introduce a new model that can be taken as the starting point for the definition of a better behaved dynamics. ..."

    I quoted the above earlier but it may have been overlooked, so I repeat the quote here. Now to these three papers we can add Giddings and Marolf

    http://arxiv.org/abs/0705.1178
    A global picture of quantum de Sitter space
    Steven B. Giddings, Donald Marolf
    17 pages, 1 figure

    "Perturbative gravity about a de Sitter background motivates a global picture of quantum dynamics in 'eternal de Sitter space,' the theory of states which are asymptotically de Sitter to both future and past. Eternal de Sitter physics is described by a finite dimensional Hilbert space in which each state is precisely invariant under the full de Sitter group. This resolves a previously-noted tension between de Sitter symmetry and finite entropy..."

    Giddings is known as a string theorist but this is not a string paper. This paper helps to build a conceptual bridge in the direction of the non-string QG community.
    Relational observables developed largely by Rovelli, play a central role here---as they do in recent work of Thiemann, Dittrich, Gambini and Pullin.

    De Sitter space is of special interest to researchers in non-string QG. You may remember that when Smolin gave an introductory course in LQG in 20-some video lectures the TEXT he used was his 2002 paper "Quantum Gravity with a Positive Cosmological Constant". The active development in DSR ("deformed special relativity) is related to the de Sitter group. (See for example the papers of Kowalski-Glikman, but almost any recent DSR paper might do.)

    So Giddings Marolf paper is right down LQG alley.:smile:

    Giddings Marolf cite many papers by people in the LQG community---four by Rovelli, several by Ashtekar, several by Ambjorn, by Thiemann, by Gambini and Pullin. Also one by Dittrich. Doubtless others, I didnt make a careful count. This paper will be of interest and will have usefulness outside of string research.

    BTW everybody knows the cliché "String War" (which seems largely to have been angry reaction to Lee Smolin's book, often without reading it, and continued loud denial of the interest and progress occurring in nonstring research). My reaction to the socalled String War has been boredom---following it would be a waste of my time. Maybe it has subsided by now.

    This paper of Gidding Marolf is what I think STRING PEACE should look like. It is written so as to not only be fundamental valuable research but also so as to build a bridge of mutal recognition between prominent people at KITP (a string research center) on the one hand and non-string QG researchers on the other.
     
    Last edited: May 10, 2007
  7. May 10, 2007 #6
    I pretty much agree with everything that Smolin has to say in his book about the string theory approach. But, looking at the recent quantum gravity developments, I think we can expect a "The trouble with quantum gravity" book within the next 10 years. :biggrin:

    Some people apparently fail to understand that new theories are developed by people with new ideas who, only afterwards, search for the proper mathematical tools to express it in, not by just digging into all kind of mathematical constructs, higher dimensions or by applying an endless barrage of different parameters in trial and error computer simulations.
    What we need is another Einstein or Newton, not a mathematician or computer programmer.
     
  8. May 10, 2007 #7

    Fra

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    I think that's well put. I always felt the common method of beeing guided by mathematical fiddling and then when you achieved mathematical consistency in some some sense, only afterwards trying to see if it has anything to do with reality and if it is also logically consistent from the realistic, as opposed to the overly idealistic viewpoint.

    I think we should start from the right end of things, if we could only find it :)

    /Fredrik
     
  9. May 10, 2007 #8

    f-h

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    I've not looked at this in depth, but if I remember correctly they are referring to some problems Rovelli et al found in the semiclassical regime. That is, perturbations around a semiclassical state do almost but not quite give the expected result.
     
  10. May 15, 2007 #9

    marcus

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    Have to add this excellent survey paper of Ashtekar to the list for 2nd quarter 2007.
    major output this quarter.

    this is the best summary of where LQG research is at present that I've seen. Invited talk at last year's Marcel Grossman Conference

    http://arxiv.org/abs/0705.2222
    Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions
    Abhay Ashtekar
    21 pages, to appear in the Proceedings of the 11th Marcel Grossmann Conference

    "As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of the status of the program by addressing some frequently asked questions. This account is addressed primarily to researchers outside the loop quantum gravity community."

    Now the list of 2nd quarter MIP candidates (with a little winnowing down) is the above Ashtekar paper plus these others:

    http://arxiv.org/abs/0705.0674
    A new spinfoam vertex for quantum gravity
    Etera R. Livine, Simone Speziale
    25 pages 6 figures

    "We introduce a new spinfoam vertex to be used in models of 4d quantum gravity ... We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations..."

    "The spinfoam formalism for loop quantum gravity (LQG) [1] is a covariant approach to the definition of the dynamics of quantum General Relativity (GR). It provides transition amplitudes between spin network states. The most studied example in the literature is the Barrett–Crane (BC) model [2]. This model has interesting aspects, such as the inclusion of Regge calculus in a precise way, but it can not be considered a complete proposal. In particular, recent developments on the semiclassical limit show that [the older BC model] does not give the full correct dynamics for the free graviton propagator [3]. In this paper we introduce a new model that can be taken as the starting point for the definition of a better behaved dynamics. ..."

    The following paper by Rovelli et al which appeared today helps to place in context the above work by Livine and Speziale:

    http://arxiv.org/abs/0705.2388
    The loop-quantum-gravity vertex-amplitude
    Jonathan Engle, Roberto Pereira, Carlo Rovelli
    6 pages

    "Spinfoam theories are hoped to provide the dynamics of non-perturbative loop quantum gravity. But a number of their features remain elusive. The best studied one -the euclidean Barrett-Crane model- does not have the boundary state space needed for this, and there are recent indications that, consequently, it may fail to yield the correct low-energy n-point functions. These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way certain second class constraints are imposed, arguably incorrectly, strongly. We present an alternative model, that can be derived as a bona fide quantization of a Regge discretization of euclidean general relativity, and where the constraints are imposed weakly. Its state space is a natural subspace of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network space. The model provides a long sought SO(4)-covariant vertex amplitude for loop quantum gravity."


    http://arxiv.org/abs/gr-qc/0703144
    Dynamical coherent states and physical solutions of quantum cosmological bounces
    Martin Bojowald
    30 pages, 3 figures

    "A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. ... an exactly solvable model ... basis for a systematic perturbation theory of loop quantum gravity... remarkably different from what is known for harmonic oscillator coherent states. ... the quantum state ... evolve deterministically through the bounce."


    http://arxiv.org/abs/0705.0006
    Multiple-event probability in general-relativistic quantum mechanics: a discrete model
    Mauricio Mondragon, Alejandro Perez, Carlo Rovelli

    ".... The model provides a tool for discussing the probabilistic interpretation of generally-covariant quantum systems, without the confusion generated by spurious infinities..."
     
    Last edited: May 16, 2007
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