标题： 静态孤立子，具有非零Hopf数 显示英文标题

标题： Static solitons with non-zero Hopf number

摘要： 我们研究了三维空间中广义非线性O(3)$\sigma$-模型，其中场是$S^3 \mapsto S^2$的映射。 这类映射由一个称为Hopf数的同伦不变量分类，该数值取整数值。 该模型展示了闭涡旋类型的孤子解，这些孤子解的能量具有较低的拓扑界限。 我们明确计算了拓扑电荷为1和2时的场，并讨论了它们的形状和结合能。 考虑了附加势项的影响，并给出了缓慢旋转孤子谱的一个近似。 显示英文摘要

摘要： We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.