A Symmetry Theorem in the Positron Theory

In the positron theory considerable interest attaches to the consideration of processes in which the occurrence of electrons and positrons is transitory only, such as the scattering of light by a Coulomb field (Delbr\"uck), and the scattering of light by light (Euler and Kockel). Calculations of such effects can frequently be simplified on account of cancellations brought about by the distribution's symmetry between electrons and positrons. An abstract proof is here presented for the theorem which predicts the appearance of such cancellations in the general case. Certain modifications are found to be required when interactions other than the usual electric forces are introduced.