Derivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra

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dc.creatorGsponer, Andre
dc.date2008-12-29
dc.date.accessioned2026-07-07T12:22:57Z
dc.date.available2026-07-07T12:22:57Z
dc.descriptionThe classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions. All calculations are made in a Colombeau algebra, and the spinor representations provided by the biquaternion formulation of classical electrodynamics are used to make all four-dimensional integrations exactly and in closed-form. The total rate of energy-momentum radiated by an arbitrarily moving relativistic point-charge under the effect of its own field is shown to be rigorously equal to minus the self-interaction force due to that field. This solves, without changing anything in Maxwell's theory, numerous long-standing problems going back to more than a century. As an immediate application an unambiguous derivation of the Lorentz-Dirac equation of motion is given, and the origin of the problem with the Schott term is explained: it was due to the fact that the correct self-energy of a point charge is not the Coulomb self-energy, but an integral over a delta-squared function which yields a finite contribution to the Schott term that is either absent or incorrect in the customary formulations.
dc.description35 pages. Long version of arXiv:0812.3493
dc.identifierhttps://arxiv.org/abs/0812.4812
dc.identifierhttp://arxiv.org/abs/0812.4812
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/213828
dc.subjectClassical Physics
dc.titleDerivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra
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