  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.
