N- and 1-time Classical Description of N-body Relativistic Kinematics and the Electromagnetic Interaction

TL;DR

This paper develops a covariant 1-time framework for describing N relativistic scalar particles with electromagnetic interactions, deriving Coulomb potential and regularizing self-energy using Grassmann charges.

Contribution

It introduces a covariant 1-time description for N-body relativistic systems with electromagnetic interactions, including a method to extract Coulomb potential and regularize self-energy.

Findings

Derived Coulomb potential from field theory.

Regularized classical self-energy using Grassmann-valued charges.

Established a covariant relativistic statistical mechanics framework.

Abstract

The intrinsic covariant 1-time description (rest-frame instant form) for N relativistic scalar particles is defined. The system of N charged scalar particles plus the electromagnetic field is described in this way: the study of its Dirac observables allows the extraction of the Coulomb potential from field theory and the regularization of the classical self-energy by using Grassmann-valued electric charges. The 1-time covariant relativistic statistical mechanics is defined.