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Quantum field theory and the Jones polynomial. (English) Zbl 0818.57014
Yang, Chen Ning (ed.) et al., Braid group, knot theory and statistical mechanics II. London: World Scientific. Adv. Ser. Math. Phys. 17, 361-451 (1994).
The paper represents an expanded version of a lecture at the IAMP Congress, Swansea, July 1988. 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 $$S^ 3$$ to arbitrary manifolds that are computable from a surgery presentation. These results shed new light on conformal field theory in $$1 + 1$$ dimensions, which can be generated essentially by studying the generally covariant $$2 + 1$$ dimensional theory on various three manifolds with boundary.
For the entire collection see [Zbl 0798.00007].

##### MSC:
 57N10 Topology of general $$3$$-manifolds (MSC2010) 57M25 Knots and links in the $$3$$-sphere (MSC2010) 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81T13 Yang-Mills and other gauge theories in quantum field theory