  The classical theory of radiating point-charges is revisited: the retarded
potentials, fields, and currents are defined as nonlinear generalized functions
and all calculations are made in a Colombeau algebra. 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.
