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Spacetime-matter degrees of freedom in current LQG research

  1. Mar 23, 2006 #1


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    For the purposes of this thread LQG is defined in a pragmatic unrigorous way. Loop gravity is what loop gravitists do.

    That begs the question who are representative loop gravitists? Well it is a fuzzy set but I think we all have an idea who they are: people like Rovelli, Smolin, Freidel, sometimes-Baez, Bojowald...
    I am leaving some big names off to give you some to think of.

    And people who co-author a lot with those people. I would include Kowalski-Glikman and Magueijo even though strictly speaking they are involved in DSR, because that is a main focus of QG phenomenology.

    The important thing in talking about Loop Gravity is that it is a DIRECTION of several related lines of investigation. And it's important to have one's eyes open and focus on what Loop people ACTUALLY DO, rather than having some artificial construct in mind about what they were doing in 1996, or what is in some book.

    So this thread is an INTERPRETIVE thread, where I am going to give you my take on the current direction(s) of research in the community of people we think of as Loop Gravity people-----to a large extent it is simply those who attended the October LOOPS '05 conference or who are co-authoring with central people at that conference, but that would have to be qualified, so I will be somewhat flexible in what Loop-and-allied work I consider.
    Last edited: Mar 23, 2006
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  3. Mar 23, 2006 #2


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    One thing I have to do is fetch links to some papers that show where the Loop Gravity community is going.

    The trend I see is people discovering that
    the fundamental degrees of freedom used to describe time and space also appear to give rise to matter as well
    In other words, macroscopic matter and geometry are increasingly seen to emerge from the same set of descriptors. so I want to illustrate that by mentioning a few recent papers. Some or all of these will have been discussed in other threads already.

    Exotic Statistics for Loops in 4d BF Theory
    John C. Baez, Derek K. Wise, Alissa S. Crans
    40 pages, many figures

    Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
    Laurent Freidel, Etera R. Livine
    46 pages
    "We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators"

    In October Freidel's Loops '05 talk was
    Effective Field theory from quantum gravity
    "The Coupling of matter fields to spin foam models of quantum gravity will be discussed. We will show in the case of three dimensional gravity how the integration of quantum gravity degrees of freedom coupled to matter can be explicitely described in terms of an effective field theory. This theory is a new non commutative field theory obeying the principle of doubly special relativity. We will conclude on the extension of this approach to the four dimensional case."

    Effective 3d Quantum Gravity and Non-Commutative Quantum Field Theory
    "We show that the effective dynamics of matter fields coupled to 3d quantum gravity is described after integration over the gravitational degrees of freedom by a braided non-commutative quantum field theory symmetric under a kappa-deformation of the Poincaré group."

    Quantum Gravity and the Standard Model
    Sundance O. Bilson-Thompson, Fotini Markopoulou, Lee Smolin
    12 pages, 21 figures

    "We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics... These are identified in terms of certain patterns of braiding of graphs,...
    These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs..."
    Last edited: Mar 23, 2006
  4. Mar 23, 2006 #3


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  5. Mar 23, 2006 #4


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    thanks f-h, I will expand these out and take a closer look. Any explaining you want to do would be very welcome, since you are doing LQG research and part of that community you can give a truer perspective on where it is going if you have time and want to, than I can.

    If you do want to take the time to explain, how does the Group Field Theory method of Krasnov and Oriti include matter?

    If you dont have the time, it's OK: I will just check these two things out and see what I make of them.

    Quantum Gravity with Matter via Group Field Theory
    Kirill Krasnov
    47 pages, many figures

    "A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point particles. The generalization considered is that of replacing the group leading to pure quantum gravity by the twisted product of the group with its dual --the so-called Drinfeld double of the group. The Drinfeld double is a quantum group in that it is an algebra that is both non-commutative and non-cocommutative, and special care is needed to define group field theory for it. We show how this is done, and study the resulting GFT models. Of special interest is a new topological model that is the "Ponzano-Regge'' model for the Drinfeld double. However, as we show, this model does not describe point particles. Motivated by the GFT considerations, we consider a more general class of models that are defined using not GFT, but the so-called chain mail techniques. A general model of this class does not produce 3-manifold invariants, but has an interpretation in terms of point particle Feynman diagrams."

    Group field theory formulation of 3d quantum gravity coupled to matter fields
    Daniele Oriti, James Ryan
    28 pages, 21 figures

    "We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs for the matter fields. The model then assigns quantum amplitudes to these fat graphs given by spin foam models for gravity coupled to interacting massive spinning point particles, whose properties we discuss."
    Last edited: Mar 23, 2006
  6. Mar 24, 2006 #5


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    I'm *starting* in LQG and have been working on the (very abstract) conceptional framework rather then anything "real" so far so I don't really know more then most other posters here.

    I have no understanding whatsoever of Krasnovs work but maybe I can say a word on Oritis stuff. GFT models provide us with Spinfoam quantizations of Gravity. The feynman expansion of the vaccuum expectation value is the spinfoam state sum. What Oriti does is build such a model for Freidels approach. This works quite elgently. The usual 3D GFT uses a field over three copies of SU(2), these produce the threevalent vertices we have in spinfoams. The field is then required to be "lorentz invariant"

    phi (g_1, g_2, g_3) = phi (a g_1,a g_2,a g_3)

    This basically is invariance under the internal gauge as far as I understand.
    The idea is now to include a matter field into the action. This should depend on the g_i but also on a fourth copy of SU(2) u. Now lorentz invariance includes the fourth copy:

    psi (g_1, g_2, g_3, u) = psi (a g_1,a g_2,a g_3,a u)

    Now the whole theory is still invariant under gauge transformation but no longer under transformations acting only on the gravitational part. Relative to the particle, gauge invariance is broken.
    Diagramatically this leads to familiar open edges. The nodes with psi are four valent and the u edge is essentially open.

    One hope is that this way one could get the non commutative field theory Freidel develops on the level of the action.
  7. Mar 24, 2006 #6


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    thanks, I see that Oriti is to give the Smolin lecture around 5 or 6 days from now. on Wednesday. I hope he discusses GFT.

    for now, i will not worry about the paper by Krasnov, and will try to better understand the Oriti-Ryan paper you mentioned
    Last edited: Mar 24, 2006
  8. Mar 25, 2006 #7
    *Roughly* speaking, I think the idea behind Krasnov's work was the following:
    Start with the Feynman series expansion of say a bosonic free field theory in 2+1 dimensions. Classically, a point particle in 2+1 (!) dimensions generates a conical singularity with a deficit angle d= 2*Pi - \psi - \psi is the circumference of the unit circle at the conical singularity - d is proportially to the mass. This means: take the orthogonal euclidean space to the momentum of the particle in Minkowski and cut out a piece of pie corresponding to d. Now, this ONLY works in 2+1 since there, gravity has no local degrees of freedom and hence no propagating gravitational waves. The introduction of a point particle simply being a *local* Ricci curvature effect (notice: we have a background spacetime on which to perform cutting and pasting procedures). Knowing this you might wonder what the effect of gravitation is on the bosonic QFT. Here the observation was that to each Feynman diagram you can attach a (closed) surface by cutting out the deficit angles at the vertices of the embedded Feynman diagram (say in the torus or R^2). That is the ``quantum gravity´´ effects are to be found at the vertices of the feynman diagrams alone. I order to remember more, I should look it up...
  9. Mar 25, 2006 #8


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    thanks Careful.
    it helps when you give a thumbnail sketch like this
    (at least it helps me and maybe others as well)

    could you please give a similar reading of the new Baez paper:
    "Four-dimensional BF theory" Baez-Wise-Crans?
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