电荷不确定性与磁单极子分裂
Charge ambiguity and splitting of monopoles
摘要：
本文致力于研究拓扑缺陷的各个方面，出现在平均场论治疗的物理系统，如超冷原子气体和规范场理论。我们首先调查拓扑电荷的歧义和拓扑电荷的添加使用覆盖空间的数学形式主义，澄清这些现象的许多方面。随后，我们分类拓扑缺陷配置由几个单极和unknotted环缺陷的同伦群和基本的群作用，从而推广了以前的分类的一个单一的单极和一个单一的unknotted环缺陷。最后，我们研究了多电荷拓扑单极子在物理系统小扰动下的衰变，并分析了多电荷拓扑单极子分裂为多个单电荷拓扑单极子的条件。
英文摘要：
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.
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