Dyons and Interactions in Nonlinear (Born-Infeld) Electrodynamics

TL;DR

This paper explores nonlinear Born-Infeld electrodynamics with dyons, revealing their interactions, angular momentum properties, and potential as models for particles like electrons, including their oscillatory behavior and possible gravitating characteristics.

Contribution

It introduces a detailed analysis of dyon interactions in Born-Infeld theory, highlighting their angular momentum, oscillatory nature, and potential as particle models with spin.

Findings

Dyons exhibit constant angular momentum independent of distance and speed.

Bidyon configurations can model particles with electron-like charge and spin.

Oscillatory behavior suggests bidyons as nonlinear oscillators and possible gravitating particles.

Abstract

Born-Infeld nonlinear electrodynamics with point singularities having both electric and magnetic charges are considered. Problem of interaction between the associated soliton dyon solutions is investigated. For the case of long-range interaction at first order by a small field of distant solitons we obtain that the generalized Lorentz force is acted on a dyon under consideration. Short-range interaction between two dyons having identical electric and opposite magnetic charges is investigated for an initial approximation. We consider the case when the velocities of the dyons have equal modules and opposite directions on a common line. It is shown that the associated field configuration has a constant full angular momentum which is independent of the interdyonic distance and their speed. This property permits a consideration of this bidyon configuration as an electromagnetic model of charged particle with spin. We numerically investigate movement of the dyons in this configuration for the case when the full electric charge equals the electron charge and the full angular momentum equals the electron spin. It is shown that for this case the absolute value of relation between electric and magnetic charges of the dyons equals the fine structure constant. The calculation gives that the bidyon may behave as nonlinear oscillator. Associated dependence of frequency on the full energy is obtained for the initial approximation. In the limits of the electrodynamic model we obtain that the quick-oscillating wave packet may behave like massive gravitating particle when it move in high background field. We discuss the possible electrodynamic world with the oscillating bidyons as particles.