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From Quantum Field Theory to Axiomatics

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1765)

Abstract

In the first part of this appendix we review the basics of the Chera-Simons topological quantum field theory in three dimensions and rational conformal field theory in two dimensions. The notions of Wilson lines in general three dimensional space-time and charges on a surface are briefly explained. We argue that continuous sewing of surfaces over charged punctures translates to gluings of three dimensional space-times along neighborhoods of Wilson lines. In the second part we discuss how the conditions on the physical models can be cast into a more formal axiomatic framework. We start with an outline of a few previous approaches to extended TQFT’s, and discuss their relations amongst each other. Finally, we explain how the double category picture summarizes and extends a formulation of extended TQFT’s given by Kazhdan and Reshetikhin.

Keywords

  • Wilson Line
  • Conformal Block
  • Conformal Field Theory
  • Morse Function
  • Abelian Category

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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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). From Quantum Field Theory to Axiomatics. In: Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners. Lecture Notes in Mathematics, vol 1765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44625-7_9

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  • DOI: https://doi.org/10.1007/3-540-44625-7_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42416-1

  • Online ISBN: 978-3-540-44625-5

  • eBook Packages: Springer Book Archive