paper

Singular Sources of Maxwell Fields with Self-Quantized Electric Charge

arXiv:physics/0308045

Abstract

Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions' distribution. Maxwell equations themselves are treated as consequences (say, integrability conditions) of a primary ``superpotential'' field subject to some nonlinear and over-determined constraints (related, in particular, to twistor structures). As the result, we obtain (in explicit or implicit algebraic form) a distinguished class of Maxwell fields, with singular sources necessarily carrying a ``self-quantized'' electric charge integer multiple to a minimal ``elementary'' one. Particle-like singular objects are subject to the dynamics consistent with homogeneous Maxwell equations and undergo transmutations -- bifurcations of different types. The presented scheme originates from the ``algebrodynamical'' approach developed by the author and reviewed in the last section. Incidentally, fundamental equivalence relations between the solutions of Maxwell equations, complex self-dual conditions and of Weyl ``neutrino'' equations are established, and the problem of magnetic monopole is briefly discussed.

25 pages, no figures. To appear in the review book "Has the Last Word been Said in Classical Electrodynamics", eds. A.Chybukalo and R. Smirnov-Rueda

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