Feynman Propagator for a System of Interacting Scalar Particles in the Fokker Theory

TL;DR

This paper develops a generalized quantum formulation for interacting scalar particles using Feynman propagators within the Fokker theory, proposing modifications to incorporate Minkowski space time coordinates.

Contribution

It introduces a new canonical formulation and a modified propagator that replaces independent proper times with Minkowski space time coordinates.

Findings

Defined the functional integral on generalized phase space.

Determined the measure in the configuration space of world lines.

Proposed a modified propagator using Minkowski space time coordinates.

Abstract

A generalized canonical formulation of the theory of the electromagnetic Fokker interaction for a system of two particles is proposed. The functional integral on the generalized phase space is defined as the initial one in quantum theory. After integration over the momenta, the measure of integration in the generalized configuration space of world particle lines is determined. The problem of dynamic interpretation of the Feynman propagator for a system of particles with independent proper time parameters is discussed. A modification of the propagator is proposed, in which the role of independent time parameters is taken by the time coordinates of the particles in Minkowski space.