A conservative stochastic Dirac-Klein-Gordon system
Analysis of PDEs
2024-05-29 v3
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.
Cite
@article{arxiv.2305.00903,
title = {A conservative stochastic Dirac-Klein-Gordon system},
author = {Evgueni Dinvay and Sigmund Selberg},
journal= {arXiv preprint arXiv:2305.00903},
year = {2024}
}