ar X iv : h ep - t h / 95 10 06 5 v 1 1 1 O ct 1 99 5 LOCALISED SOLUTIONS OF THE DIRAC - MAXWELL EQUATIONS

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: • Spherical symmetry necessitates the existence of a magnetic monopole. • There exists a uniquely defined solution, determined only by the demand that the solution be analytic at infinity. • The equations describe highly compact objects with an inner onion like shell structure .