Modified scattering for the three dimensional Maxwell-Dirac system

Abstract: In this work we prove global well-posedness for the massive Maxwell-Dirac equation in the Lorentz gauge in $\mathbb{R}^{1+3}$, for small and localized initial data, as well as modified scattering for the solutions.  In doing so, we heuristically exploit the close connection between massive  Maxwell-Dirac and the  wave-Klein-Gordon equations, while  developing a novel approach which applies directly at the level of the Dirac equations.  This is joint work with Sebastien Herr and Martin Spitz.