Singular Sources of Maxwell Fields with Self-Quantized Electric Charge

Details Singular Sources of Maxwell Fields with Self-Quantized Electric Charge Singular Sources of Maxwell Fields with Self-Quantized Electric Charge

2003-08-11

arxiv.org/abs/physics/0308045v1

"Has the Last Word been Said on Classical Electrodynamics?", eds. A.Chubykalo, V.Onoochin, A.Espinoza, V.Smirnov-Rueda. - Rint

Physics

Classical Physics

25 pages, no figures. To appear in the review book "Has the Last Word been Said in Classical Electrodynamics", eds. A.Chybukal

Scientific paper

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.

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