The Classical Equations of Motion of Point Particles. II

Abstract

In Part I of this paper the problem of the relation of field theory and the theory of action at a distance was investigated for the neutral vector and scalar meson theories. The work is here extended to the charge-symmetrical meson theory. First the equations of motion of particles interacting through vector meson fields are found for half-retarded, half-advanced interaction, using the field-theoretical methods developed for retarded interaction; equations for both cases are given for particles interacting through scalar meson fields. These equations contain integrals over the past and entire motion in the retarded and symmetric case, respectively. These are inadmissible from the point of view of action at a distance, and new equations are postulated. Variational principles are developed for these equations, and energy-momentum tensors and charge-current vectors guaranteeing detailed conservation laws are defined. The application of the Wheeler-Feynman method to the equations of both theories is discussed. Conclusions analogous to those found in the neutral case are obtained.