2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56940The 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.19 pages LaTex (amsart) Typos corrected, theorem 3 proof improved. No change to resultsMathematical Physics35Q40 (Primary), 00A79 (Secondary)text