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The classical theory of radiating point-charges is revisited: the retardedpotentials, fields, and currents are defined as nonlinear generalizedfunctions. All calculations are made in a Colombeau algebra, and the spinorrepresentations provided by the biquaternion formulation of classicalelectrodynamics are used to make all four-dimensional integrations exactly andin closed-form. The total rate of energy-momentum radiated by an arbitrarilymoving relativistic point-charge under the effect of its own field is shown tobe rigorously equal to minus the self-interaction force due to that field. Thissolves, without changing anything in Maxwell's theory, numerous long-standingproblems going back to more than a century. As an immediate application anunambiguous derivation of the Lorentz-Dirac equation of motion is given, andthe origin of the problem with the Schott term is explained: it was due to thefact that the correct self-energy of a point charge is not the Coulombself-energy, but an integral over a delta-squared function which yields afinite contribution to the Schott term that is either absent or incorrect inthe customary formulations.

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