The extended local gauge invariance and the BRS symmetry in stochastic quantization of gauge fields

We investigate the BRS invariance of the first-class constrained systems in the context of the stochastic quantization. For the first-class constrained systems, we construct the nilpotent BRS transformation and the BRS invariant stochastic effective action based on the (D+1)-dimensional field theoretical formulation of stochastic quantization. By eliminating the multiplier field of the gauge-fixing condition and an auxiliary field, it is shown that there exists a truncated BRS transformation which satisfies the nilpotency condition. The truncated BRS invariant stochastic action is also derived. As examples of the general formulation, we investigate the BRS invariant structure in the massless and massive Yang-Mills fields in stochastic quantization. (orig.)