The Stochastic Quantization Method in Phase Space and a New Gauge Fixing Procedure

Abstract

We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are automatically selected and introduced by imposing stochastic consistency conditions upon the first class constraints. Then the equilibrium solution of the Fokker-Planck equation is identical with corresponding path integral distribution.