Dirac-Maxwell solitons

Detailed analysis of the coupled Dirac-Maxwell equations and the structure of their solutions is presented. Numerical solutions of the field equations in the case of spherical symmetry with negligible gravitational self-interaction reveal the existence of families of solitons with electric-field dominance that are completely determined by the observed charge and mass of the underlying particles. A soliton is found which has the charge and mass of the electron as well as a charge radius of ${10}^{-23}\hspace{0.5em}\mathrm{m}.$ This is well within the present experimentally determined upper limit of $\simeq {10}^{-18}\hspace{0.5em}\mathrm{m}.$ Properties of these particles as well as possible extension to the work herein are discussed.