Quantum field theory and the Jones polynomial

Edward Witten

Research output: Contribution to journalArticlepeer-review

3091 Scopus citations

Abstract

It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized from S3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.

Original languageEnglish (US)
Pages (from-to)351-399
Number of pages49
JournalCommunications In Mathematical Physics
Volume121
Issue number3
DOIs
StatePublished - Sep 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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