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Communications in Mathematical Physics

, Volume 156, Issue 3, pp 435–472 | Cite as

Chern-Simons theory with finite gauge group

  • Daniel S. Freed
  • Frank Quinn
Article

Abstract

We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the “Verlinde formula”. The careful development may serve as a model for dealing with similar issues in more complicated cases.

Keywords

Neural Network Statistical Physic Hilbert Space Field Theory Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Daniel S. Freed
    • 1
  • Frank Quinn
    • 2
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA
  2. 2.Department of MathematicsVirginia Polytechnical InstituteBlacksburgUSA

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