Semiclassical Asymptotics for the Maxwell - Dirac System

TL;DR

This paper develops a rigorous semiclassical analysis of the coupled Maxwell-Dirac system using nonlinear WKB methods, providing insights into the behavior of solutions at small scale ratios.

Contribution

It introduces a novel nonlinear WKB analysis for the Maxwell-Dirac system, advancing understanding of semiclassical limits in quantum field models.

Findings

Established local-in-time semiclassical asymptotics

Derived critical order solutions of O(√ε)

Provided a rigorous mathematical framework for the analysis

Abstract

We study the coupled system of Maxwell and Dirac equations from a semiclassical point of view. A rigorous nonlinear WKB-analysis, locally in time, for solutions of (critical) order $O(\sqrt{\epsilon})$ is performed, where the small semiclassical parameter $\epsilon $ denotes the microscopic/macroscopic scale ratio.