Abstract

A model of the quantum hydrodynamics of a charged particle in an external electromagnetic field is considered with account for the spin–orbit interaction and the influence of the Zeeman energy. The model is based on the formalism of introducing non-Abelian Yang–Mills gauge fields. It is shown that non-Abelian gauge fields generate forces, that act on the spin and spin current. It is demonstrated that the helicity of a particle moving on the background of such fields, that create forces that depend on the spin of the particle, is not conserved. A two-fluid model of quantum hydrodynamics is developed for systems of electrons in spin-up and spin-down states moving against the background of the magnetic structure of a skyrmion with a nontrivial topology. A system of continuity equations, momentum balance, and evolution equations of spin density is constructed, and the helicity conservation for electron fluxes is proved in the framework of the proposed two-fluid model.

中文翻译：

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凝聚态和螺旋性守恒理论中的规范领域

摘要

考虑了自旋轨道相互作用和塞曼能量的影响，考虑了外部电磁场中带电粒子的量子流体动力学模型。该模型基于引入非阿贝尔杨格斯米勒规范场的形式主义。结果表明，非阿贝尔规范场会产生作用于自旋和自旋电流的力。证明了在这样的场的背景下移动的粒子的螺旋度是不守恒的，其产生依赖于粒子自旋的力。针对处于自旋向上和自旋向下状态的电子系统，在具有非平凡拓扑结构的天体的磁性结构的背景下移动，开发了一种量子流体动力学的双流体模型。连续性方程组，动量平衡，