A Note on Positron Theory and Proper Energies

Abstract

The origin of the infinite light-quantum proper energy which follows, according to Heisenberg, from the creation of matter by the field of the photon, is examined in some detail. We are led to investigate the inconsistencies which appear on the incorporation of the Dirac positron theory into the formalism of the quantum theory. These inconsistencies make it impossible to regard with confidence any predictions of the theory for which a consideration of the singularities of the density matrix is essential. It is shown that when the off-diagonal distance in the density matrix is taken different from zero, the proper energy of a light quantum and the electromagnetic energy of an electron are, in order $e^2$, finite, and that the off-diagonal distance plays in these calculations the part of a generalized electron radius.