Localised Solutions of the Maxwell-Dirac Equations

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Referee this paper: arXiv:hep-th/9510065 by Chris Radford

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The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case of {\em spherical symmetry}. These static spherically symmetric equations are examined in some detail and a numerical solution presented. Some surprising results emerge:
* 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.