The Classical Equations of Motion of Point Particles. I

Abstract

The problem of the relation of field theory and action at a distance is investigated for the neutral vector and scalar meson theories. The equations of motion of point particles with half-advanced, half-retarded inter-action are found using the field theoretical methods developed for retarded interaction; they include an integral over the entire motion of the particle in analogy to an integral over the past motion in the retarded case. These are inadmissible from the point of view of action at a distance and a new set of equations is postulated. This new set is derivable from a variational principle analogous to Fokker's in electrodynamics for the symmetric case, and energy-momentum tensors guaranteeing the conservation laws can be defined. The application of the Wheeler-Feynman method to the equations of the symmetric case leads to the equations of the retarded case only for the field theoretical equations, but to slightly different ones for those of action at a distance. Some implications of these results are discussed.