A conservative stochastic Dirac-Klein-Gordon system

Abstract

Considered herein is a particular nonlinear dispersive stochastic system consisting of Dirac and Klein-Gordon equations. They are coupled by nonlinear terms due to the Yukawa interaction. We consider a case of homogeneous multiplicative noise that seems to be very natural from the perspective of the least action formalism. We are able to show existence and uniqueness of a corresponding Cauchy problem in Bourgain spaces. Moreover, the regarded model implies charge conservation, known for the deterministic analogue of the system, and this is used to prove a global existence result for suitable initial data.