Charge ambiguity and splitting of monopoles

This paper focuses on topological defects, appearing in mean-field-theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We begin by investigating the 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.

Automated summary

This paper focuses on topological defects in mean-field-theory treatments of physical systems. The ambiguity and addition of topological charges are investigated using the mathematical formalism of covering spaces, clarifying many aspects of these phenomena. Topological-defect configurations consisting of several monopoles and unknotted ring defects are classified in terms of homotopy groups and fundamental-group actions, generalizing previous classifications. The decay of multiply charged topological monopoles under small perturbations and the conditions for their splitting into singly charged monopoles are analyzed.