Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge

TL;DR

This paper explores the stability of electric charges using nonlinear electrodynamics, specifically Born-Infeld theory, revealing internal structures and magnetic effects that could explain charge stability.

Contribution

It introduces a classical model with magnetic excitations in nonlinear electrodynamics that accounts for charge stability through self-interaction mechanisms.

Findings

Magnetic excitations can stabilize electric charges.

Explicit analytic solutions for fields are derived.

Magnetic contributions exert negative pressure balancing electric repulsion.

Abstract

The present work proposes a discussion on the self-energy of charged particles in the framework of nonlinear electrodynamics. We seek magnet- ically stable solutions generated by purely electric charges whose electric and magnetic fields are computed as solutions to the Born-Infeld equa- tions. The approach yields rich internal structures that can be described in terms of the physical fields with explicit analytic solutions. This suggests that the anomalous field probably originates from a magnetic excitation in the vacuum due to the presence of the very intense electric field. In addition, the magnetic contribution has been found to exert a negative pressure on the charge. This, in turn, balances the electric repulsion, in such a way that the self-interaction of the field appears as a simple and natural classical mechanism that is able to account for the stability of the electron charge.