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New Majid Algebraic QG papers (Oriti book)

  1. Apr 19, 2006 #1


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    Algebraic approach to quantum gravity II: noncommutative spacetime
    S. Majid
    26 pages, 2 figures; book chapter to appear in D. Oriti, ed., Cambridge Univ. Press
    "We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a thorough account of the bicrossproduct model noncommutative spacetimes of the form [t,x_i]=i lambda x_i and the correct formulation of predictions for it including a variable speed of light. We also study global issues in the Poincaré group in the model with the 2D case as illustration. We show that any off-shell momentum can be boosted to infinite negative energy by a finite Lorentz transformaton."

    Algebraic approach to quantum gravity III: noncommmutative Riemannian geometry
    S. Majid
    25 pages, 1 figure; to appear in collection B. Fauser and J. Tolksdorf, eds., Birkhauser

    "This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that arises naturally as the classical limit; a theory with nonsymmetric metric and a skew version of metric compatibilty. Meanwhile, in quantum gravity a key ingredient of our approach is the proposal that the differential structure of spacetime is something that itself must be summed over or 'quantise' as a physical degree of freedom. We illustrate such a scheme for quantum gravity on small finite sets."


    remember this connection with QG from earlier this year:
    Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity
    L. Freidel, S. Majid
    54 pages, 2 figs
    We show that the *-product for U(su_2) arising in [ref. EL] in an effective theory for the Ponzano-Regge quantum gravity model is compatible with the noncommutative bicovariant differential calculus previously proposed for 2+1 Euclidean quantum gravity using quantum group methods in [ref. BatMa]..."

    Freidel is at Perimeter/Lyon and refs are to Freidel-Livine and Majid-Batista.
    contact between GFT spinfoam approach and noncommutative geometry.

    I do not know what is #1 of this series----we have only paper II and paper III AFAIK

    here are the first four refs in the paper Majid has provided as chapter for Oriti book:

    [1] G. Amelino-Camelia and S. Majid. Waves on noncommutative space-time and gamma ray bursts. Int. J. Mod. Phys. A 15:4301–4324, 2000.

    [2] E. Batista and S. Majid. Noncommutative geometry of angular momentum space U(su2). J. Math. Phys. 44 (2003) 107-137.

    [3] L. Freidel and E. R. Livine, “Ponzano-Regge model revisited. III: Feynman diagrams and effective field theory,” hep-th/0502106.

    [4] S. Majid and L. Freidel. Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity, hep-th/0601004. [5]

    this can help give an idea what Shahn Majid is talking about here and where it fits in.

    IMHO dynamite
    Last edited: Apr 19, 2006
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  3. Apr 19, 2006 #2


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    Majid shows the empirical testability flag

    In roman two, early on he says this:

    ...Note that although (1) breaks usual Poincaré invariance, Special Relativity still holds as the quantum group ‘symmetry’. This is also the first noncommutative spacetime model with a genuine physical prediction[1], namely a variable speed of light (VSL). The NASA GLAST satellite to be launched in 2007 may among other things be able to test this prediction through a statistical analysis of gamma-ray bursts even in the worst case that we might expect for the parameter lambda ~10^-44 s ( the Planck timescale).

    my bolding
    Last edited: Apr 19, 2006
  4. Apr 20, 2006 #3


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    Today Loll posted the title of the talk which Laurent Freidel is to give at Utrecht on 1 May.

    Grafiti no.123 Laurent Freidel (Perimeter I.): Non-commutative effective field theory and quantum gravity

    the most recent Freidel paper is discussed here:

    I believe the "hidden QG" results of Freidel-Baratin to be significant (see the linked thread) and note that the analysis requires a deformation of Poincaré symmetry that was already foreseen and studied by Shahn Majid more than 10 years ago. And it is precisely the non-commutative geometry aspect that makes Freidel's results potentially testable by GRB observation.

    (this assumes that Freidel-Baratin can extend their analysis to 4D, which they say in their last paper they can do---and have in preparation)
    Last edited: Apr 20, 2006
  5. Apr 23, 2006 #4


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    Majid says he plans a series of three papers all about ALGEBRAIC APPROACH TO QUANTUM GRAVITY, and he has posted AQG II and AGQ III, and he says about the remaining AQG I that it is more about the philosophy.

    I think in this case what philosophy means is themes he talks about briefly at the beginning in the other papers, before delving into detail.

    Like for example
    where does non-commutative geometry fit in
    why to expect a non-continuum model of space and time
    why gravity has proven intractible til now

    So we can get an idea of his philosophy, that he will be explaining in the forthcoming AQG I paper, just by sampling exerpts of the two papers we already have, which I'll do now.
  6. Apr 23, 2006 #5


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    AQG II:
    "In this article we present noncommutative geometry(NCG) not as a ‘theory of everything’ but as a bridge between any future, perhaps combinatorial, theory of quantum gravity and the classical continuum geometry that has to be obtained in some limit. We consider for the present that NCG is simply a more general notion of geometry that by its noncommutative nature should be the correct setting for the phenomenology and testing of first next-to-classical quantum gravity corrections. Beyond that, the mathematical constraints of NCG may give us constraints on the structure of quantum gravity itself insofar as this has to emerge in a natural way from the true theory."

    So he is suggesting to look at NCG not as a TOE but as a bridge that could help some possibly COMBINATORIAL QG theory (e.g. spinfoam, triangulations) to get a good classical limit. In fact NCG is playing exactly this role with spinfoam in recent work of Majid, Freidel, Livine where it is like a MEDIATOR between spinfoam QG and the flat case.

    Here is another quote.

    ---quote AQG III---
    Why is quantum gravity so hard? Surely it is because of its nonrenormalisable nature leading to UV divergences that cannot be tamed. However, UV divergences in quantum field theory arise from the assumption that the classical configurations being summed over are defined on a continuum. This is an assumption that is not based on observation but on mathematical constructs that were invented in conjunction with the classical geometry visible in the 19th century. A priori it would therefore be more reasonable to expect classical continuum geometry to play a role only in a macroscopic limit and not as a fundamental ingredient.

    While this problem might not be too bad for matter fields in a fixed background, the logical nonsensicality of putting the notion of a classical manifold that is supposed to emerge from quatum gravity as the starting point for quantum gravity inside the functional path integral, is more severe and this is perhaps what makes gravity special.

    The idea of course is to have the quantum theory centred on classical solutions but also to take into account nearby classical configurations with some weight. However, taking that as the actual definition is wishful and rather putting ‘the cart before the horse’.

    Note that string theory also assumes a continuum for the strings to move in, so does not address the fundamental problem either.
  7. Apr 24, 2006 #6


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    this all goes back to a key short paper of Freidel Livine
    http://arxiv.org/hep-th/0512113 [Broken]
    Effective 3d Quantum Gravity and Non-Commutative Quantum Field Theory

    before, we only had to worry about ONE "classical limit"
    and now there are two different limits that a QG theory should get right
    the Freidel Livine December 05 paper is really essential and clear and I urge anyone who has not already to read it

    Notice top right column of page 2 where it describes the two different limits. This is TWO requirements that a QG theory must meet, so it is more stringent and therefore more helpful.

    A. KEEP HBAR CONSTANT and let G go to zero. This is the "zero gravity limit" that several Freidel papers refer to. what one expects to get is USUAL FEYNMAN DIAGRAMS OF usual special relativistic QFT. Or as Freidel Livine put it "we expect to recover standard relativistic quantum field theory in this regime".

    B. Let hbar and G BOTH GO TO ZERO TOGETHER, in such a way that the Planck mass stays constant. Then one gets what they call a semiclassical limit which is expected to be a NONCOMMUTATIVE FLAT GEOMETRY some form of DSR.

    You can easily see how that goes on page 2 of the paper, in the 3D case. But also, since Freidel is working on the 4D case, let's check how it would be in 4D.

    then Planck mass is [tex]\sqrt{\hbar c/G}[/tex]

    so it is easy just keep G and hbar proportional and both -> 0
    then the mass will stay constant.

    and also as a byproduct Planck length goes to zero
    because it is [tex]\sqrt{\hbar G/c^3}[/tex]
    and that is good because Planck length going to zero corresponds to an idea of emerging smooth manifold classical limit. The continuum picture emerges as the Planck length vanishes.
    Last edited by a moderator: May 2, 2017
  8. Apr 24, 2006 #7


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    IMO the December 05 paper of Freidel Livine raises the bar of what a QG theory is supposed to do and if one can use the jazzy word "paradigm" then yes that is what it provides.

    But hey, Freidel may FAIL to achieve in 4D what he and Livine got in 3D.

    BTW oddly enough Freidel Livine were using the 1948 PONZANO-REGGE model. Someone was saying that Irish and Italians are very good in geometry and wondering if it was their Catholicism (all kinds of things one hears on the internet.) Tulio Regge became an EU Senator.

    Well the 1948 PonzRegge model was just about the first QG model ever written (THE first says Freidel) and I guess what they did in 2005 was they UNDERSTOOD it better (after almost 60 years).

    Anyway Freidel may fail to extend it to 4D and then it will not raise the bar. But if he succeeds then I think that will significantly change the picture of what a QG theory is supposed to do.

    then it should have a DSR or NCG "semiclassical" limit with G and hbar going to zero and it should also have a "zero gravity" limit which is usual QFT.

    We had some talk about PHENOMENOLOGY lately on the Bee thread and I did not say my personal prejudice of what is interesting in QG Pheno.
    I dont have to say my personal feelings because other people like Bee are the experts and it was their thread.

    But if I were working in the field of QG Pheno, I believe I would focus on testing DSR (with maybe a little MOND as well). The DSR or NCG issues are the prime up-front issues and they relate to what Freidel is doing (and Majid and others)

    the MOND business is a sleeper. It may turn out to have something to do with QG, perhaps by way of DSR. As could the cosmological constant.
    Last edited: Apr 24, 2006
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