Global strong solution to Maxwell-Dirac equations in 1+1 dimensions

TL;DR

This paper proves the global existence and uniqueness of solutions for the Maxwell-Dirac equations with nonzero charge mass in one spatial dimension, under the Lorentz gauge, ensuring well-posedness of the initial value problem.

Contribution

It establishes the first rigorous proof of global solutions for the 1+1 dimensional Maxwell-Dirac system with nonzero charge mass.

Findings

Global existence of solutions is proven.

Uniqueness of solutions is established.

Solutions exist for all time in the specified function spaces.

Abstract

The Maxwell-Dirac equations with nonzero charge mass in one space dimension are studied under the Lorentz gauge condition. The global existence and uniqueness of solution in $C([0,+\infty);L^2(R^1))\times C_b(R^1 \times [0,\infty))$ for initial value problem of Maxwell-Dirac equations are proved.