The Stationary Maxwell-Dirac Equations
Chris Radford
Abstract
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≤ E≤ 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.
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