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A TQFT From Purely Mathematical Considerations

  1. May 1, 2017 #1
    I worked my way through this paper

    http://www.math.harvard.edu/theses/senior/lee/lee.pdf

    as part of a mathematics reading project and believe I have a fairly good understanding of the material. There is virtually no physics in this paper yet we seem to arrive at Dijkgraaf-Witten Theory quite naturally at the end of the paper. I find the idea, if true, that purely mathematical considerations can lead to the notion of gauge theory from physics quite amazing. I say, "if true" because other than teaching myself a little bit of QM and GR my knowledge of physics is quite limited. So my questions are, how widely accepted is Dijkgraaf-Witten Theory in the physics community? I hear it's tied to things like string theory, is that true? Dijkgraaf-Witten Theory seems to be an attempt to tie together GR and QM, is that a fair assessment?

    Edit: Fixed some typos
     
    Last edited: May 1, 2017
  2. jcsd
  3. May 2, 2017 #2

    A. Neumaier

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    It is too low-dimensional to be ''real'' physics but it is well established within theoretical physics as a class of toy examples that help to gain a better understanding of more realistic examples. You can read more in http://https://ncatlab.org/nlab/show/Dijkgraaf-Witten+theory [Broken] and in the original article by Dijkgraaf and Witten,
    Dijkgraaf, Robbert, and Edward Witten. "Topological gauge theories and group cohomology." Communications in Mathematical Physics 129.2 (1990): 393-429.

    Note also that gauge theory, although originating in physics, is a purely mathematical concept from the differential geometry of vector bundles.
     
    Last edited by a moderator: May 8, 2017
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