Quantum field theory and the Jones polynomial
Abstract
It is shown that 2+1 dimensional quantum YangMills theory, with an action consisting purely of the ChernSimons 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 S ^{3} 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 September 1989
 DOI:
 10.1007/BF01217730
 Bibcode:
 1989CMaPh.121..351W