Stochastic Quantization of Non-Abelian Gauge Field: Unitarity Problem and Faddeev-Popov Ghost Effects

Abstract

The stochastic quantization method is applied to the non-Abelian gauge field up to the second order perturbation. It is shown that the stochastic quantization method automatically produces the same correct results as given by the well-known Faddeev-Popov trick but never requires to introduce artificially any ghost field. The gauge fixing problem in this method is also examined in detail. Finally preliminary discussions are given as to whether the physical state condition is automatically satisfied.