The Chern-Simons path integral is one of the most interesting examples for the usefulness of heuristic path integral expressions. In a famous paper Edward Witten was able to compute the so-called "Wilson loop observables" of Chern-Simons theory explicitly at a heuristic level. The explicit values he obtained are given by highly non-trivial link invariants including the Jones polynomial. The elaboration of Witten's ideas later lead to a breakthrough in knot theory, the discovery of the universal Vassiliev invariant.
It would be desirable to establish the connection between the Chern-Simons path integral and the aforementioned link invariants at a rigorous level. In my talk I will review some recent process in this direction. |