Gauge Fixing Condition as Non-Holonomic Constraint in Stochastic Quantization of Non-Abelian Gauge Fields

Abstract

In stochastic quantization of non-Abelian gauge fields, we introduce a sort of non-holonomic constraint working as a covariant gauge fixing condition in the Langevin equation, and show that the new condition kills fictitious time-dependent divergent terms keeping the gauge invariance and the unitarity without help of any ghost field. The procedure also suggests us a possible way of quantizing non-holonomic systems.