自旋规范场：从Berry相到拓扑自旋输运和霍尔效应
Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
摘要：
本文研究了具有n个不同本征值的矩阵哈密顿量描述的自旋粒子演化过程中规范场的出现。通过引入一个自旋规范场，一个具有自旋的粒子可以被描述为一个非阿贝尔纯规范场U（n）中标量粒子的自旋多重态.结果，我们可以建立一个关于群U^n（1）的规范不变的粒子演化理论。因此，在绝热（阿贝尔）近似中，自旋规范场是粒子扩展相空间上n个电磁场U（1）的模拟。这些场都是力场，它们的作用力进入本文以一般形式导出的粒子运动方程。运动方程描述了拓扑自旋输运、抽运和分裂。在这个理论中，贝瑞相的表示类似于电磁场中粒子的狄拉克相。由于与电磁场的类比，该理论在四维形式中变得自然。除了一般理论的文章认为一些重要的特殊的例子，已知的和新的。
英文摘要：
The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U(n). As the result, one can create a theory of particle evolution that is gauge invariant with regards to the group U^n(1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U(1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory the article considers a number of important particular examples, both known and new.
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