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Major paper by Fairbairn-a way to put matter into 4D quantum gravity

  1. Jul 21, 2008 #1


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    Major paper by Fairbairn--a way to put matter into 4D quantum gravity

    I expect this paper will "raise the dead" in the sense of evoking a comment from John Baez :-). It develops some lines of research he was working on three years ago.
    It references work by Derek Wise, a Baez PhD----also Freidel, Baratin, Livine, Perez...
    Freidel et al got matter to arise very nicely in 3D quantum gravity, even found Feynman diagrams hiding in the spinfoams. But then it seemed to stop---couldn't get it to work in 4D.

    In any case this is a really interesting 30-page paper
    On gravitational defects, particles and strings
    Winston J. Fairbairn
    30 pages
    (Submitted on 20 Jul 2008)

    "We study the inclusion of point and string matter in the deSitter gauge theory, or MacDowell-Mansouri formulation of four dimensional gravity. We proceed by locally breaking the gauge symmetries of general relativity along worldlines and worldsheets embedded in the spacetime manifold. Restoring full gauge invariance introduces new dynamical fields which describe the dynamics of spinning matter coupled to gravity. We discuss the physical interpretation of the obtained formalism by studying the flat limit and the spinless case on arbitrary backgrounds. It turns out that the worldline action describes a massive spinning particle, while the worldsheet action contains the Nambu-Goto string augmented with spinning contributions. Finally, we study the gravity/matter variational problem and conclude by discussing potential applications of the formalism to the inclusion of the Nambu-Goto string in spinfoam models of four dimensional quantum gravity."

    Sample exerpt from introduction:

    "Our common quantum relativistic understanding of matter in terms of finite dimensional, irreducible representations of the Poincare algebra is a very rough approximation of reality. This description is tied to the isometries of the flat, Minkowski solution to general relativity and yields a good approximation only in very weak gravitational fields, like for instance, in our particle accelerators where the successes of quantum field theory have been crowned.

    In a fundamental theory of Nature, one cannot expect this approximation to be valid since in the early, Planckian universe, spacetime is undoubtedly not flat. Accordingly, the search of the fundamental structure of matter is tied to non-trivial, and certainly quantum configurations of the gravitational field. In turn, a complete theory of quantum gravity will have to incorporate a precise description of the degrees of freedom of matter.

    As a first step, it seems therefore natural to look for an understanding of matter which does not rely on a particular fixed background geometry at the classical level. This will automatically render the formulation compatible with non-perturbative attempts to the quantisation of gravity which cannot, consistently, rely on a fixed, background metric structure.

    A very old and appealing idea consists in considering the Einstein equations as defining the notion of matter. In other words, to consider matter as particular, possibly singular, configurations of the gravitational field. In this framework, we are reversing the standard picture where matter is defined on flat spacetime and then tentatively extended to other solutions of general relativity. Here, we are starting from the gravitational perspective, without selecting a preferred solution, and deriving matter from the geometry of spacetime. Obviously, this formulation should reproduce the standard properties of matter in the flat limit, but will also select a preferred formulation from the gravitational perspective. For example, such a reversed approach has recently led to conceptually and technically strong results regarding the coupling of matter to three dimensional quantum gravity [2], [3].

    The concrete implementation of this procedure relies on a the gauge symmetries of gravity,..."
    Last edited: Jul 21, 2008
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  3. Jul 21, 2008 #2


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    Re: Major paper by Fairbairn--a way to put matter into 4D quantum gravity

    Winston Fairbairn was one of Rovelli's bunch, at Marseille. We first heard of him when he co-authored a really interesting paper with Rovelli, as a PhD student IIRC, back around 2004. We actually had a thread about it here at PF back then. Now he is in John Barrett's group at Nottingham. There is a possibility here that one can get some stringy things to happen in the context of 4D quantum gravity without all those extra dimensions. A spinfoam is a 2D critter living in 4D spacetime and thus is second cousin to a worldsheet. It's possible, stranger things have happened :wink:
    To give a little more of a taste of the paper, here is from conclusions, on page 28:

    6 Conclusion

    In this paper, we have studied the inclusion of point and string matter in fourdimensional general relativity recasted as a deSitter gauge theory. We proceeded by introducing local symmetry breaking terms in the action supported by worldlines and worldsheets. Restoration of full gauge invariance has led to the introduction of new dynamical fields interpreted as describing matter degrees of freedom. The diffeomorphism symmetry led us to the notion of position or embedding, while the local Lorentz symmetry gave rise to variables encoding momentum and spin. This physical interpretation was established by relating our formalism to the description of particle and string theories in terms of Poincar´e group coordinates, or pseudo-classical variables `a la Balachandran and collaborators. We have then studied the variational problem of the coupled system. We have calculated the deformation of the momentum and total angular momentum conservation laws due to curved spacetime effects. This has led us to Mathisson-Papapetrou and spin precession equations both for particles and strings. We have then derived the equations describing the gravitational field produced by such matter sources. For the non-spinning string case, we have discussed some solutions related to cosmic strings. Finally, we have explained why this formulation of (spinless) strings was promising from the spinfoam quantum
    gravity perspective.

    We believe that the framework presented here provides potentially interesting outcomes in various directions of research, the investigations of which are currently under study.

    Fairbairn's reference [27] is to a followup paper that he is doing with Roberto Pereira (Marseille).

    I'm late for supper. have to go. back later.
    Last edited: Jul 21, 2008
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