Stochastic quantization in field theory with a fundamental mass

Stochastic quantization of fermions is developed in the framework of quantum field theory with non-Euclidean momentum space. Analogs of the Langevin and Fokker–Planck equations taking into account the new geometrical properties of the momentum space are obtained by using Grassmann variables to describe the non-Euclidean Fermi fields. It is shown that the stochastic method and the second-quantization method are equivalent in path-integral terms.