A Solution of the Maxwell-Dirac Equations in 3+1 Dimensions

TL;DR

This paper explores specific localized solutions to the Maxwell-Dirac equations in four-dimensional spacetime, revealing bound states influenced mainly by their self-generated electric fields.

Contribution

It presents a novel class of stationary, localized solutions to the Maxwell-Dirac system, advancing understanding of self-consistent field configurations.

Findings

Identification of discrete energy eigenstates

Solutions are primarily bound by self-produced electric fields

Advances in numerical methods for nonlinear field equations

Abstract

We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced electric field.