Charge ambiguity and splitting of monopoles

TL;DR

This paper explores topological charge ambiguity, classifies complex monopole configurations, and analyzes the stability and splitting behavior of multiply charged monopoles in physical systems.

Contribution

It introduces a mathematical framework for understanding charge ambiguity, classifies multi-monopole configurations, and studies conditions for monopole splitting.

Findings

Charge ambiguity clarified via covering space formalism

Classification of multi-monopole configurations using homotopy groups

Conditions identified under which multiply charged monopoles split

Abstract

This paper is dedicated to studying various aspects of topological defects, appearing in mean-field theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We start by investigating topological charge ambiguity and addition of topological charges using the mathematical formalism of covering spaces, which clarifies many aspects these phenomena. Subsequently, we classify topological defect configurations consisting of several monopoles and unknotted ring defects in terms of homotopy groups and fundamental group actions on them, thus generalizing the previous classifications of a single monopole and a single unknotted ring defect. Finally, we examine the decay of multiply charged topological monopoles under small perturbations of the physical system, and analyze the conditions under which multiply charged monopoles are inclined to split into several singly charged monopoles.