A class of physically acceptable, classical, relativistic, many-particle Lagrangians

Abstract

It is shown that the Fokker–Wheeler–Feynman theory for relativistic, massive, charged point particles interacting via action-at-a-distance forces of electromagnetic origin can be generalized to define a class of model systems all with the same physically acceptable properties. These properties include the satisfaction of the correct Lorentz covariance, time-reversal symmetry, particle-interchange symmetry, and causality. For closed systems there exists a generalized Hamiltonian function, linear momentum, and angular momentum that are constants of the motion. This generalization thus yields a relativistic, dynamic description of this class, analogous to nonrelativistic classical mechanics. Included in this class, within the appropriate limits, are the so-called linear relativistic scalar and vector interactions. It is anticipated that this work will be useful for the examination and understanding of physical systems, both classically and quantum mechanically, insofar as they can be modelled from a classical approach.