Global solvability of massless Dirac-Maxwell systems

TL;DR

This paper proves the global existence and uniqueness of solutions for the massless Dirac-Maxwell equations on asymptotically flat backgrounds, with potential extensions to related gauge theories.

Contribution

It establishes a global well-posedness result for the massless Dirac-Maxwell system on asymptotically flat spacetimes, extending to Dirac-Higgs-Yang-Mills theories.

Findings

Global existence and uniqueness for small initial data

Applicable to Dirac-Higgs-Yang-Mills theories

Methodology can be extended to other gauge theories

Abstract

We consider the Cauchy problem of massless Dirac-Maxwell equations on an asymptotically flat background and give a global existence and uniqueness theorem for initial values small in an appropriate weighted Sobolev space. The result can be extended via analogous methods to Dirac-Higgs-Yang-Mills theories.