Localized solutions of the Dirac–Maxwell equations

Abstract

The full classical Dirac–Maxwell equations are considered in a somewhat novel form and under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is static. A further reduction of the equations is made under the assumption of spherical symmetry. These static spherically symmetric equations are examined in some detail and a numerical solution presented. Some surprising results emerge from this investigation: (i) Spherical symmetry necessitates the existence of a magnetic monopole. (ii) There exists a uniquely defined solution, determined only by the demand that the solution be analytic at infinity. (iii) The equations describe highly compact objects with an inner onion like shell structure.