On a relation between Maxwell and Dirac theories

Abstract

It is shown that the Dirac equation can be written in a form similar to Maxwell equations, where the Maxwell tensor is written as a bilinear expression of the Dirac field and the current is a simple function of the external potential and the Dirac field. Similarly, the Maxwell equations can be written as a self-coupled Dirac equation where the potential is a simple function of the Dirac field itself. It is illustrated by examples how the new formalism helps to find solutions of the coupled field equations.