The Stationary Maxwell-Dirac Equations

Details The Stationary Maxwell-Dirac Equations The Stationary Maxwell-Dirac Equations

2001-12-18

arxiv.org/abs/math-ph/0112037v4

Physics

Mathematical Physics

19 pages LaTex (amsart) Typos corrected, theorem 3 proof improved. No change to results

Scientific paper

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.

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