Electromagnetic field theory without divergence problems: 1. The Born Legacy

TL;DR

This paper develops a consistent classical relativistic electrodynamics framework using nonlinear Maxwell--Born--Infeld equations for spinless charges, addressing divergence issues and exploring charge-free solitons and the role of Born's constant.

Contribution

It introduces a fully consistent classical relativistic electrodynamics model with nonlinear field equations and Hamilton--Jacobi charge dynamics, incorporating the Pauli principle and analyzing soliton solutions.

Findings

Classical evolution governed by Maxwell--Born--Infeld equations.

Hamilton--Jacobi law describes charge motion.

Charge-free solitons, if they exist, have enormous peak fields.

Abstract

A fully consistent classical relativistic electrodynamics with spinless point charges is constructed. The classical evolution of the electromagnetic fields is governed by the nonlinear Maxwell--Born--Infeld field equations, the classical evolution of the point charges by a many-body Hamilton--Jacobi law of motion. The Pauli principle for bosons can be incorporated in the classical Hamilton--Jacobi formalism. The Cauchy problem is explained and illustrated with examples. The question of charge-free field solitons is addressed also and it is shown that if they exist, their peak field strengths must be enormous. The value The value of Born's constant is shown to be a subtle open issue.