We study the solution of non-relativistic approximation of Dirac equation in the presence of non-Abelian external fields. The dynamics of the system is described by the Pauli Hamiltonian for a spin one-half particle carrying a non-Abelian charge. This non-Abelian charge, at the quantum level, is proportional to the generators of the U (2) gauge group and reveals the effect of a spin-orbit coupling across the non-Abelian gauge field. By choosing a suitable non-Abelian gauge field, the total angular momentum is the conserved quantity of the system as well as the corresponding supercharge. The Hamiltonian of the system is then invariant under the transformations generated by the supercharge. This allows us to apply the algebraic method. The Landau levels obtained are deformed by the non-Abelian contribution of the gauge potential. Each of these energy levels are doubly degenerate except the lowest Landau level whose eigenvalue is zero. In the Abelian limit, the Landau level e...

中文翻译：

---

保利哈密顿量，用于在非阿贝尔外场存在的情况下带有非阿贝尔电荷的自旋二分之一粒子

我们研究了在非阿贝尔外场的情况下狄拉克方程的非相对论逼近解。保利·哈密顿量描述了带有非阿贝尔电荷的自旋二分之一粒子的系统动力学。这种非阿贝尔电荷在量子水平上与U（2）规范组的生成器成比例，并揭示了非阿贝尔规范场上自旋轨道耦合的影响。通过选择合适的非阿贝尔规范场，总角动量即为系统的守恒量以及相应的增压量。然后，系统的哈密顿量在增压产生的变换下是不变的。这使我们可以应用代数方法。所获得的Landau能级因规范势的非阿贝尔贡献而变形。除了本征值为零的最低朗道能级之外，这些能级中的每一个都被双重简并。在阿贝尔（Abelian）极限中，兰道（Landau）等级...