Stochastic Coupling of Fermions

TL;DR

This paper develops a stochastic quantization approach for fermion fields, analyzing their long-term behavior and establishing existence and uniqueness of the limiting field in a first-order approximation.

Contribution

It introduces a novel stochastic quantization method for fermions starting from Dirac equations and proves the existence and uniqueness of the long-time limit.

Findings

Free fermions vanish in the long time limit

Proper combinations of fermion components behave as scalar bosons

Existence and uniqueness of the long-term limit are established in first-order approximation

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.