Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-03-03
J.Math.Phys. 35 (1994) 5219-5246
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, 11 figures
Scientific paper
10.1063/1.530749
We use Feynman diagrams to prove a formula for the Jones polynomial of a link derived recently by N.~Reshetikhin. This formula presents the colored Jones polynomial as an integral over the coadjoint orbits corresponding to the representations assigned to the link components. The large $k$ limit of the integral can be calculated with the help of the stationary phase approximation. The Feynman rules allow us to express the phase in terms of integrals over the manifold and the link components. Its stationary points correspond to flat connections in the link complement. We conjecture a relation between the dominant part of the phase and Milnor's linking numbers. We check it explicitly for the triple and quartic numbers by comparing their expression through the Massey product with Feynman diagram integrals.
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