A classical model for the Maxwell equations coupled with matter

TL;DR

This paper introduces a simple classical model coupling Maxwell's equations with a Klein-Gordon matter field, demonstrating the existence of stable hylomorphic solitons that behave like charged particles at low energy.

Contribution

It presents a novel, simplified model showing how stable solitons emerge from Maxwell-Klein-Gordon interactions, linking energy/charge ratio to particle-like behavior.

Findings

Existence of stable hylomorphic solitons in the model

Low-energy solitons behave as pointwise charged particles

Model demonstrates linear and nonlinear interactions producing solitons

Abstract

We present a simple model of interaction of the Maxwell equations with a matter field defined by the Klein-Gordon equation. A simple linear interaction and a nonlinear perurbation produce solutions of the equations containing hylomorphic solitons, namely stable, solitary waves whose existence is related to the ratio energy/charge. These solitons, at low energy, behave as poinwise charged particles in an electromagnetic field.