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Vassiliev Knot Invariants and Chern-Simons Perturbation Theory to All Orders

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Abstract:

At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot invariants. Moreover these are finite type invariants whose order coincides with the order in the perturbative expansion. Together they combine to give a universal Vassiliev invariant.

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Authors and Affiliations

  1. Institut für Theoretische Physik, ETH-Hönggerberg, CH-8093 Zürich, Switzerland, , , , , , CH

    Daniel Altschuler

  2. Laboratoire de Physique Théorique ENSLAPP, Ecole Normale Supérieure de Lyon, 46, allée d'Italie, 9364 Lyon Cedex 07, France, , , , , , FR

    Laurent Freidel

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  1. Daniel Altschuler
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  2. Laurent Freidel
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Received: 26 March 1996 / Accepted: 7 November 1996

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Altschuler, D., Freidel, L. Vassiliev Knot Invariants and Chern-Simons Perturbation Theory to All Orders . Comm Math Phys 187, 261–287 (1997). https://doi.org/10.1007/s002200050136

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  • DOI: https://doi.org/10.1007/s002200050136

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