Stochastic quantization with fermions

The method of stochastic quantization of euclidean quantum field theory is extended to the case of theories with fermion fields. A modified Langevin equation for spinors is introduced, and the corresponding master equation for the stochastic probability distribution is derived. The formal solution of this generalized Fokker-Planck equation is constructed, and the convergence towards a thermodynamic equilibrium is demonstrated. We illustrate the method in a perturbative setting by one-loop calculations in a (anti psiω)2 theory and in gauge theories. (orig.)