STOCHASTIC QUANTIZATION OF TOPOLOGICAL FIELD-THEORY

A Euclidean topological action is always purely imaginary; its stochas tic quantization inevitably involves the complex Langevin equation. We show that the standard results for abelian Chern-Simons theory can be reproduced in the stochastic approach with the Maxwell term as a regu larization; but if one ignores the factor of i, the Langevin equation will become pathological. Simplification may occur if one uses the gen eralized Langevin equation with an appropriate, purely imaginary kerne l; we exemplify this by stochastic quantization in Minkowski space-tim e and again the abelian Chern-Simons theory. The stochastic perturbati on theory of non-abelian Chern-Simons theory is also studied and the c ontributions of usual Faddeev-Popov ghosts are verified to be reproduc ible without gauge fixing.