Electrodynamic Limit in a Model for Charged Solitons

TL;DR

This paper explores a topological soliton model where charged particles have finite mass and quantized charge, showing that in the electrodynamic limit, the model simplifies to Maxwell's equations, linking topology to electromagnetic forces.

Contribution

It introduces a soliton-based model with quantized charge and demonstrates its reduction to Maxwell's equations in the electrodynamic limit, connecting topology with classical electromagnetism.

Findings

Coulomb and Lorentz forces arise from topology.

In the electrodynamic limit, the model reduces to Maxwell's equations.

Homogeneous electric fields can be expressed via the soliton field.

Abstract

We consider a model of topological solitons where charged particles have finite mass and the electric charge is quantised already at the classical level. In the electrodynamic limit, which physically corresponds to electrodynamics of solitons of zero size, the Lagrangian of this model has two degrees of freedom only and reduces to the Lagrangian of the Maxwell field in dual representation. We derive the equations of motion and discuss their relations with Maxwell's equations. It is shown that Coulomb and Lorentz forces are a consequence of topology. Further, we relate the U(1) gauge invariance of electrodynamics to the geometry of the soliton field, give a general relation for the derivation of the soliton field from the field strength tensor in electrodynamics and use this relation to express homogeneous electric fields in terms of the soliton field.