Properties of the solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
Robert T. Glassey, John Chadam · Proceedings of the American Mathematical Society · 1974
Solutions of the Maxwell-Dirac equations coupled through the standard electromagnetic interaction are shown to blow up at each spatial point for large times. This is used to show that these solutions do not tend asymptotically to free solutions. In addition it is used to prove that these equations do not admit a nontrivial stationary solution.