The Stationary Maxwell-Dirac Equations

The Maxwell-Dirac equations are the equations for electronic matter, the "classical" theory underlying QED. In this article we examine the stationary Maxwell-Dirac equations under weak regularity and decay assumptions. We prove that: There are no embedded eigenvalues in the essential spectrum, \(-m\leq E\leq m\). If \(|E|< m\) then the Dirac field components (and their derivatives) decay exponentially at spatial infinity. If \(E|=m\) then the system is "asymptotically" static and decays exponentially if the total charge is non-zero.