Point Charge in the Born-Infeld Electrodynamics

TL;DR

This paper demonstrates that the Born-Infeld nonlinear electromagnetic equations, combined with a specific boundary condition, can deterministically define a point particle’s trajectory without traditional equations of motion, advancing the theory of particle-field interactions.

Contribution

It introduces a boundary condition that allows for a deterministic description of point particles in nonlinear electromagnetism without explicit equations of motion.

Findings

The theory is perfectly deterministic with the boundary condition.

Particle trajectories are determined solely by the field equations and boundary conditions.

This approach advances the consistent modeling of point particles in nonlinear electromagnetic theories.

Abstract

We show that the nonlinear Born-Infeld field equations supplemented by the "dynamical condition" (certain boundary condition for the field along the particle's trajectory) define perfectly deterministic theory, i.e. particle's trajectory is determined without any equations of motion. It is a first step towards constructing the consistent theory of point particles interacting with nonlinear electromagnetism.