From soft Dirac monopoles to the Dirac equation

TL;DR

This paper explores the connection between topological monopoles with soft cores and the Dirac equation, demonstrating how the latter emerges as a limit of the former in both free and interacting cases.

Contribution

It introduces a model of topological particles with dual Dirac monopoles and derives the Dirac equation as a limiting case of these monopoles approaching singularities.

Findings

Derivation of the Dirac equation from topological monopoles

Demonstration of the limit where soft monopoles become singular

Application to both free and interacting particle cases

Abstract

In the model of topological particles we have four types of topologically stable dual Dirac monopoles with soft core and finite mass. We discuss the steps how to get a Dirac equation for these particles. We show for the free and the interacting case that we arrive at the Dirac equation in the limit, where the soft solitons approach singular dual Dirac monopoles.