On the Self-Energy and the Electromagnetic Field of the Electron

Abstract

The charge distribution, the electromagnetic field and the self-energy of an electron are investigated. It is found that, as a result of Dirac's positron theory, the charge and the magnetic dipole of the electron are extended over a finite region; the contributions of the spin and of the fluctuations of the radiation field to the self-energy are analyzed, and the reasons that the self-energy is only logarithmically infinite in positron theory are given. It is proved that the latter result holds to every approximation in an expansion of the self-energy in powers of $\frac{e^2}{\mathrm{hc}}$. The self-energy of charged particles obeying Bose statistics is found to be quadratically divergent. Some evidence is given that the "critical length" of positron theory is as small as $\frac{h}{\mathrm{}\left(\mathrm{mc}\right)\mathrm{}}·\exp \left(\frac{-hc}{e^2}\right)$.