Functional Integration and the Kontsevich Integral

1998/11/23 by Louis H. Kauffman, Kauffman, Louis H.
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA

paper · pdf · doi:10.48550/arxiv.math/9811137

34 pages, 14 figures, LaTeX document. Postscript file also available from http://math.uic.edu/~kauffman

arxiv created 1998/11/25 · arxiv updated 2009/11/30

Abstract

This paper is an exposition of heuristics related to Witten's functional integral, relating it to Vassiliev invariants and to the Kontsevich integrals that can be used to produce Vassiliev invariants of knots and links.In particular, we give a simplified version of the appearance of the Kontsevich integrals in the perturbation expansion of the functional integral.

Related

• The loop expansion of the Kontsevich integral, the null move and S-equivalence
• On configuration space integrals for links
• Linking coefficients and the Kontsevich integral
• Explicit formulas for the Vassiliev knot invariants
• The lines of the Kontsevich integral and Rozansky's rationality conjecture