Numerical Evaluation of a Soliton Pair with Long Range Interaction

TL;DR

This paper numerically evaluates the interaction energy of topological soliton pairs, revealing deviations from Coulomb potential at short distances and comparing these with quantum electrodynamics predictions.

Contribution

It introduces a numerical method to analyze soliton pair interactions, accounting for finite size effects and deviations from classical Coulomb behavior.

Findings

Deviations from Coulomb potential at a few soliton radii

Numerical results align with the running coupling in perturbative QED

Finite size of solitons causes measurable interaction differences

Abstract

Within the model of topological particles (MTP) we determine the interaction energy of monopole pairs, sources and sinks of a Coulombic field. The monopoles are represented by topological solitons of finite size and mass, described by a field without any divergences. We fix the soliton centres in numerical calculations at varying distance. Due to the finite size of the solitons we get deviations from the Coulomb potential at distances of a few soliton radii. We compare the numerical results for these deviations with the running of the coupling in perturbative QED.