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 r0, 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 r0 similar to that of Lorentz is obtained, in which only odd powers of r0 occur. The first term endows the electron with a mass component of electromagnetic origin. For accelerations small compared with the characteristic frequency l/r0 of the electron, the Lorentz-Dirac equations are a good approximation; for larger accelerations, higher terms become important.