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      Vassiliev Invariants and the Loop States in Quantum Gravity

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          Abstract

          An exposition of Vassiliev invariants is given in terms of the simplest approach to the functional integral construction of link invariants from Chern-Simons theory. This approach gives the top row evaluations of Vassiliev invariants for the classical Lie algebras, and a neat point of view on the results of Bar-Natan. It also clarifies the relation between Vassiliev invariants and the extension of the bracket invariant to links with transverse double points that appears in the work of Bruegmann, Gambini and Pullin on the loop representation of quantum gravity. We see that the Vassiliev vertex is not just a transversal intersection of Wilson loops, but rather has the structure of Casimir insertion (up to first order of approximation) coming from the difference formula in the functional integral. (Figures are available from the author.)

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          Quantum field theory and the Jones polynomial

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            Index for subfactors

            V. Jones (1983)
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              A polynomial invariant for knots via von Neumann algebras

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                Author and article information

                Journal
                25 October 1993
                Article
                gr-qc/9310035
                92fcd79d-e952-45b5-b181-c3ed6c652e70
                History
                Custom metadata
                22 pages, to appear in Knots and Quantum Gravity, ed. John Baez, Oxford University Press, LaTeX
                gr-qc

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