The Klein-Gordon field and a relativistic particle as a system

Abstract

A system which is composed of a Klein-Gordon field and a relativistic particle is studied as a singular system using the Hamilton-Jacobi formulation. The system is identified as a free particle, with position four-vector x(mu), conserved linear momentum B-mu, and angular-momentum tensor M-mu nu, without canonical quantization. Four-vectors x(mu) have proper Poisson bracket relations with B-mu exhibiting the fact they are real position four-vector components, not continuous indices on the mechanical variables.