A normalized solitary wave solution of the Maxwell-Dirac equations

TL;DR

This paper establishes the existence of normalized solitary wave solutions for the Maxwell-Dirac equations and positive energy minimizers for the Coulomb-Dirac model, advancing understanding of fermionic field interactions.

Contribution

It proves the existence of solitary wave solutions in the Maxwell-Dirac equations and energy minimizers in the Coulomb-Dirac model, which are new results in mathematical physics.

Findings

Existence of $L^2$-normalized solitary wave solutions for Maxwell-Dirac equations.

Existence of positive energy minimizers for Coulomb-Dirac model.

Results contribute to the mathematical understanding of fermionic field interactions.

Abstract

We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer.