The Lorentz-Dirac equation and positive-definite energy in classical electrodynamics

Abstract

We show that, in a previously developed theory of classical electrodynamics, whereeach charged classical electron has itsown electromagnetic field (and the mutual interactions between a given charge and the field of another charge make up the elementary interactions of the theory), the requirement of positive-definite total energy automatically yields the generalized form of the Lorentz-Dirac equation of motion for the charges. This occurs without the presence of direct self-interactions, hence the theory is finite and consistent without the need of infinite-renormalization techniques. The proof that this new classical electrodynamic formalism produces the same class of equations of motion, as that of renormalized Maxwell-Lorentz theory (without infinities from an internal positive-definite energy criteria), suggests that an attempt to quantize the new formalism might lead to a better formulation of quantum electrodynamics.