Yang-Mills-Higgs模型中非零Hopf不变量的拓扑孤子
Topological Soliton with Nonzero Hopf Invariant in Yang-Mills-Higgs Model
摘要：
本文对3+ 1维非阿贝尔规范理论与标量场耦合问题提出了一个具有非零Hopf不变量的拓扑孤子或瞬子解。这个解，我们称之为霍普夫孤子，代表了一个时空事件，它使粒子发生$2π$旋转。虽然这种孤子的作用是几何发散的，但在有限尺寸的系统中，它仍然可以作出相应的贡献。由于连续$U(1)$规范场的Chern-Simons项可能出现在低能有效理论中，所以Hopf孤子可能产生单极子的分数阶统计.
英文摘要：
We propose a topological soliton or instanton solution with nonzero Hopf invariant to the 3+1D non-Abelian gauge theory coupled with scalar fields. This solution, which we call Hopf soliton, represents a spacetime event that makes a $2π$ rotation of the monopole. Although the action of this Hopf soliton is logarithmically divergent, it may still give relevant contributions in a finite-sized system. Since the Chern-Simons term for the unbroken $U(1)$ gauge field may appear in the low energy effective theory, the Hopf soliton may possibly generate fractional statistics for the monopoles.
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