Classical electrodynamics without singularities

Abstract

It is shown that it is possible to construct a theory of the electron with an extended charge distribution in a Lorentz invariant way by introducing a four-dimensional form function. The electromagnetic field quantities reduce to those given by the ordinary theory at distances large compared with the electron radius r 0 , but remain finite on the world line. The equations of motion, after elimination ’of the self field, become integro-differential equations. In the case of small accelerations an expansion in powers of r 0 similar to that of Lorentz is obtained, in which only odd powers of r 0 occur. The first term endows the electron with a mass component of electromagnetic origin. For accelerations small compared with the characteristic frequency l/ r 0 of the electron, the Lorentz-Dirac equations are a good approximation; for larger accelerations, higher terms become important.