A covariant formulation of classical electrodynamics for charges of finite extension

Abstract

A covariant formulation of classical electrodynamics for charges of finite extension is developed. The nonelectromagnetic forces necessary for stability are taken into account implicitly by requiring that the charge distribution retain a given shape throughout the course of its motion; a general prescription is given for constructing charge-current densities appropriate to such rigid charge distributions. A detailed treatment of the relativistic kinematics of rotating rigid bodies is presented and application is then made to obtain, from an action principle, the equations of motion for a spherically symmetric charge distribution interacting with an applied field; the associated conservation theorems relating to the linear and angular momentum are discussed. Finally, approximations to the equations of motion are obtained by making perturbation expansions in powers of the size of the charge distribution.