The Stationary Maxwell-Dirac Equations
Abstract
Description
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.
19 pages LaTex (amsart) Typos corrected, theorem 3 proof improved. No change to results
19 pages LaTex (amsart) Typos corrected, theorem 3 proof improved. No change to results