Classical Motion of an Extended Charged Particle

Abstract

The classical equations of motion of an extended particle are re-examined and methods are found which eliminate the usual difficulties with the $\frac{4}{3}$ factor, runaway solutions, and preacceleration. Point particles are not considered, but rather localized, nonsingular distributions. The $\frac{4}{3}$ factor is eliminated by using Dixon's method for deriving the macroscopic equations of motion, while runaway solutions and preacceleration are eliminated by retaining the structure-dependent terms that the Dirac equation neglects. Finally, it is shown that in the limit of slowly varying external forces, these solutions become identical to those obtained from the integral form of the Dirac equation.