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Witten's identity for Chern-Simons theory
Authors:Bernd Brügmann
Affiliation:(1) Max-Planck-Institute of Physics, 80805 Munich, Germany
Abstract:We present a simple heuristic calculational scheme to relate the expectation value of Wilson loops in Chern-Simons theory to the Jones polynomial. We consider the exponential of the generator of homotopy transformations which produces the finite loop deformations that define the crossing change formulas of knot polynomials. Applying this operator to the expectation value of Wilson loops for an unspecified measure, we find a set of conditions on the measure and the regularization such that the Jones polynomial is obtained.
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