The Chern-Simons path integral and the quantum Racah formula

Details The Chern-Simons path integral and the quantum Racah formula The Chern-Simons path integral and the quantum Racah formula

2006-11-30

arxiv.org/abs/math-ph/0611084v1

Physics

Mathematical Physics

27 pages, 5 figures

Scientific paper

We generalize several results on Chern-Simons models on Sigma x S1 in the so-called "torus gauge", which were obtained recently in arXiv:math-ph/0507040, to the case of general (simply-connected simple compact) structure groups and general link colorings. In particular, we give a non-perturbative evaluation of the Wilson loop observables corresponding to a special class of simple but non-trivial links and show that their values are given by Turaev's shadow invariant. As a byproduct we obtain a heuristic path integral derivation of the quantum Racah formula.

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