  The theory of point-particles in classical electrodynamics has a well-known
problem of infinite self-energy, and the same is true of quantum
electrodynamics. Instead of concluding that there is no such thing as a true
point-particle, it is shown here how to remove the infinities by supposing that
the electromagnetic field tensor has a symmetric part. This does not change the
physics, as the equation of motion and the antisymmetric part of the retarded
fields appearing in the equation of motion are unaffected. The symmetric part
of the field tensor is not observable and therefore it need not be
gauge-invariant, whereas the antisymmetric part is observable, gauge-invariant,
and satisfies both the Maxwell Equations and the field equations governing the
whole field tensor. This approach goes well beyond prior efforts at classical
renormalization, and also entails a new derivation and generalization of the
Lorentz-Abraham-Dirac (LAD) equation of motion.
