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Derivation of the total twist from Chern-Simons theory

Allen C. Hirshfeld·Uwe Sassenberg
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Abstract

The total twist number, which represents the first non-trivial Vassiliev knot invariant, is derived from the second order expression of the Wilson loop expectation value in the Chern-Simons theory. Using the well-known fact that the analytical expression is an invariant, a non-recursive formulation of the total twist based on the evaluation of knot diagrams is constructed by an appropriate deformation of the knot line in the three-dimensional Euclidian space. The relation to the original definition of the total twist is elucidated.

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Allen C. Hirshfeld, Uwe Sassenberg. 1995-02-14. Derivation of the total twist from Chern-Simons theory. https://arxiv.org/abs/hep-th/9502088

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