Reshetikhin’s formula for the Jones polynomial of a link: Feynman diagrams and Milnor’s linking numbers

Feynman diagrams are used to prove a formula for the Jones polynomial of a link derived recently by 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...

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Bibliographic Details
Published in:Journal of mathematical physics 1994-10, Vol.35 (10), p.5219-5246
Main Author: Rozansky, L.
Format: Article
Language:English
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Summary:Feynman diagrams are used to prove a formula for the Jones polynomial of a link derived recently by 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 one 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. A relation between the dominant part of the phase and Milnor’s linking numbers is conjectured. It is checked explicitly for the triple and quartic numbers by comparing their expression through the Massey product with Feynman diagram integrals.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.530749