The Lienard-Wiechert Potential of Charged Scalar Particles and their Relation to Scalar Electrodynamics in the Rest-Frame Instant Form

TL;DR

This paper explores the Lienard-Wiechert potentials for charged scalar particles within a new instant form of dynamics, addressing causality issues and connecting scalar electrodynamics with a covariant rest-frame description.

Contribution

It introduces a covariant rest-frame instant form of dynamics and analyzes scalar particles with electromagnetic fields, resolving causality problems at the pseudoclassical level.

Findings

Lienard-Wiechert potentials evaluated for scalar particles

Causality issues of Abraham-Lorentz-Dirac equation addressed

Connection established between scalar electrodynamics and particle-field system

Abstract

After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar particles with pseudoclassical Grassmann-valued electric charges plus the electromagnetic field are studied. The Lienard-Wiechert potentials of the particles are evaluated and it is shown how the causality problems of the Abraham-Lorentz-Dirac equation are solved at the pseudoclassical level. Then, the covariant rest-frame description of scalar electrodynamics is given. Applying to it the Feshbach-Villars formalism, the connection with the particle plus electromagnetic field system is found.