Problems Connected with the Prohibition of Self-Interactions in Integro-Causal Quantum Field-Theory

Abstract

The electrostatic self-energy of an electron is a quantity based on a wrong formulation of electrodynamics for elementary particles. Omission of the electrostatic self-energy from the formalism of quantum electrodynamics destroys the covariance of the theory, unless one postulates at the same time the absence of self-interaction of electrons through the photon field. This makes the theory integro-causal. Also self-interactions interrupted by other interactions are to be prohibited, if the covariance is to be maintained. The Lamb shift and similar effects then require the introduction of additional interaction terms. Conservation of probability shows that the exclusion of all self-interactions would also cancel the transition probabilities for real physical phenomena. In order to avoid this, the prohibition of self-interactions is to be restricted to those with virtual intermediate states, in which the unperturbed energy is too much different from the energy of the initial (not of the just preceding) state. The problem of expressing this restriction in a covariant form has not yet been solved.