Stochastic quantization of axial vector gauge theories with fermions

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory (CQFT) in higher orders. It has been suggested that some of these new features might give rise to a mechanism to explain tiny fermion masses as arising due to radiative corrections. Some features of U(1) axial vector gauge theory in Parisi Wu stochastic quantization are reported. These features are not absent if the theory is formulated in the conventional way. In particular we present arguments for renormalizability of the massive axial vector gauge theory coupled to a massless fermion.