Stochastic Quantization of the Chern-Simons Theory

We discuss Stochastic Quantization of $d$=3 dimensional non-Abelian Chern-Simons theory. We demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the correct propagator. We also analyze the connection between $d$=3 Chern-Simons and $d$=4 Topological Yang-Mills theories showing the equivalence between the corresponding regularized partition functions. We study the construction of topological invariants and the introduction of a non-trivial kernel as an alternative regularization.Comment: 30 page