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Dittrich's "Continuum Limit of LQG" is a landmark paper

  1. Sep 29, 2014 #1

    marcus

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    People interested in quantum gravity research may wish to take note of Dittrich's September 2014 paper which I believe represents a significant step towards constructing the continuum limit and the physical Hilbert space of LQG. It will be on the third quarter MIP poll. I'll get the link.

    http://arxiv.org/abs/1409.1450
    http://inspirehep.net/search?p=find eprint 1409.1450
    The continuum limit of loop quantum gravity - a framework for solving the theory
    Bianca Dittrich
    (Submitted on 4 Sep 2014)
    The construction of a continuum limit for the dynamics of loop quantum gravity is unavoidable to complete the theory. We explain that such a construction is equivalent to obtaining the continuum physical Hilbert space, which encodes the solutions of the theory. We present iterative coarse graining methods to construct physical states in a truncation scheme and explain in which sense this scheme represents a renormalization flow. We comment on the role of diffeomorphism symmetry as an indicator for the continuum limit.
    18 pages, 1 figure, for a volume edited by A. Ashtekar and J. Pullin, to be published in the World Scientific series "100 Years of General Relativity"
     
    Last edited: Sep 29, 2014
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  3. Sep 29, 2014 #2

    marcus

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    Reference [46] in Dittrich's paper is to a followup she did with two other authors, providing supportive detail. Since that also just came out this month I will post the link to that as well:
    http://arxiv.org/abs/1409.2407
    http://inspirehep.net/search?p=find eprint 1409.2407
    Decorated tensor network renormalization for lattice gauge theories and spin foam models
    Bianca Dittrich, Sebastian Mizera, Sebastian Steinhaus
    (Submitted on 8 Sep 2014)
    Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. Using this novel information encoded in the decoration might eventually lead to new methods incorporating both analytical and numerical techniques.
    14 pages, 12 figures.

    Notice that in order to accomplish the continuum limit one must devise coarse-graining and refining methods which do not depend on having a prior metric.
    The role that "decorated tensor network renormalization" plays is explained concisely in the main paper in section 5
    The particular role played by the Dittrich Mizera Steinhaus work [46] is discussed in that section in the first paragraph of page 11.

    The main paper (1409.1450) seems to serve as a helpful guide to how the various pieces fit together, without burdening the reader with too much detail.
     
    Last edited: Sep 29, 2014
  4. Sep 29, 2014 #3

    marcus

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    BTW I just checked back in the biblio thread and in both cases it was Atyy who spotted these papers and added them to our LQG-related bibliography. These and several more that Atty spotted will be on the MIP poll for the July-September period, which should be posted in a day or two.
     
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