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Can LSS unification (gravity, gauge, Higgs) be quantized à la new LQG ?

  1. Aug 23, 2010 #1

    marcus

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    Can LSS unification (gravity, gauge, Higgs) be quantized à la "new LQG"?

    This came out in April. We had it on our second quarter MIP ("most important paper") poll.
    https://www.physicsforums.com/showthread.php?t=413838
    So far, this is a classical treatment. And it uses a spacetime manifold. The basic playground is a manifold M with a principle G-bundle over M where G can be, for example, Spin(1+N,3). This how I read it anyway.

    We know that in some cases we can start with that kind of picture and in the course of constructing a quantum version, get a "manifoldless spacetime" picture using graphs, spin networks and spinfoams. Then, instead of a spatial or spacetime continuum one has (for each graph) a group manifold---a finite cartesian product of the basic group G. These provide a way to set up graph Hilbert spaces and then one takes a projective limit.

    I haven't thought about how much of that might go over using a different group such as Spin(1+N,3).

    I just toss this out in case anyone wants to have a look at the Lisi, Smolin, Speziale paper and speculate about a "manifoldless" quantum version in the style of the new formulation of LQG we got in http://arxiv.org/abs/1004.1780
     
    Last edited: Aug 23, 2010
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  3. Aug 23, 2010 #2

    marcus

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    Re: Can LSS unification (gravity, gauge, Higgs) be quantized à la "new LQG"?

    Just to be clear about it, in case a new person does not realize this, when I say "quantize" I do not mean in any conventional textbook sense. I mean construct a quantum version of the "new LQG" kind that has the right limit behavior---corresponding to what you started with.

    By way of illustration: contemporary LQG is not some sort of methodical quantization of Ashtekar General Relativity (the connection version of classical GR). The field did indeed start out in the 1990s based on Ashtekar GR. But convergence of various attempts crystalized in a de novo reformulation different from, but combining aspects of each. Something like a leap occurred, as is described in the survey/status report http://arxiv.org/abs/1004.1780.

    In other words, can you adapt http://arxiv.org/abs/1004.1780 to achieve a quantum theory version of the Lisi Smolin Speziale unification?
     
    Last edited: Aug 23, 2010
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