The electromagnetic energy of a point charge

Abstract

There are many regions for preferring the point model of the electron, in which the field equations of empty space hold all the way up to the centre of the electron, to the Lorentz model, in which the charge is distributed over a small sphere. The point model is not without difficulties, however, and two have attracted special attention. The first is that the field becomes infinite at the charge, so that the Lorentz equations of motion cannot be applied directly; the second is that the ordinary expression leads to an infinite electromagnetic energy in the neighbourhood of the charge. As these difficulties occur both in classical and in quantum electrodynamics it seems reasonable to look for their solution, first in the classical theory, and then try to translate it into the quantum theory. A recent paper by Dirac (1938) has satisfactorily removed the first difficulty from the classical theory. The present paper shows how the second can be removed also. The translation of these methods to quantum theory has not yet been accomplished. Some papers by Wentzel (1933, 1934) have also dealt with this subject, both from the classical and the quantum standpoint, but they do not seem to be altogether without difficulties, and the method is rather complicated to use in actual problems.