The classical equations of a point particle in a symmetric meson field

Abstract

The equations of motion of a point particle interacting with charge symmetrical mesons are deduced on the action-at-a-distance theory from a variation principle which is analogous to that of Fokker in electrodynamics. In the first article an action is first defined with the help of a Riesz function in terms of a parameter a to be determined by the method of analytical continuation. It is then shown that by expressing the mesic charge-current and dipole densities with the help of a Riesz function which for a →2 behaves like Dirac's d-function, the adjunct fields, which are introduced on purely formal grounds, satisfy the fundamental equations of meson field in the usual field theory for a →2. The variation of the action function for a ?2 finally gives the required equations of motion. In the second article the adjunct fields, which are singular on the world line of the particle, are evaluated by Riesz method of analytical continuation for a →2. The scattering of mesons by nucleons are calculated in the last article.