Abstract

The Parisi-Wu stochastic quantization method is extended to a new method in the phase space. We first show that this method applied to a regular dynamical system yields the equilibrium distribution, in the stochastic process with respect to a fictitious time, which is the same formula as given by the conventional path-integral method. Next we present an extension of this phase space formulation applicable to non-Abelian gauge systems. The generalized Fokker-Planck equation gives naturally the equilibrium distribution which coincides with the Faddeev-Popov formula. The relation between this method and stochastic gauge fixing schemes is briefly discussed.

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