Stochastic Coupling of Fermions

Abstract

The stochastic quantization of the fermion field is performed starting from Dirac equations. The statistical properties of stochastic terms in Langevin equations are described by explicit formulae of a Markov process. The interaction of the field is introduced as correlation of the stochastic terms. In the long time limit free fermions disappear and proper combinations of field components propagate as a scalar boson field. The existence and uniqueness of the long time limit is proved in the first order approximation of stochastic Liouville equation.