Introduction

In classical theory, the field strengths E and H become arbitrarily large in the neighborhood of the point-charge e, so that the integral over the energy density 1/8π(E2 + H2) diverges. To overcome this difficulty, one therefore assumes a finite radius r0 for the electron in classical electron theory. This radius is related to the mass m of the electron in the order-of-magnitude relation r0 ~ e2/mc2; the integral over the energy density is then of the order mc2. In quantum theory, not only this radius r0 but possibly also another length λ0 = h/mc, which is characteristic of the electron, plays a role in the self-energy. In a superficial consideration in terms of the correspondence principle, one would suspect that the self-energy of the point-like electron must also become infinite in quantum theory.

In fact, Oppenheimer and Waller have indeed shown that a perturbation method which proceeds in powers of e does not yield finite values for the self-energy. At first, it appears as if, in quantum theory also, only the introduction of a finite electron radius can provide a way out of this difficulty.