论文标题
从欧几里得对称性的Landau水平的无限退化，重新审视了中央扩展
Infinite degeneracy of Landau levels from the Euclidean symmetry with central extension revisited
论文作者
论文摘要
在针对开始研究生水平的教学环境中探索了平面兰道系统的平面兰道系统，该系统描述了带有均匀磁场的带电粒子的量子机械运动。已知该系统将欧几里得对称性具有两个维度，其中中央扩展名$ \ bar {e}（2）$。在本文中，我们通过利用相关的$ \ bar {e}（2）$对称代数来重新访问该系统（称为Landau级别）的著名能量特征值。具体来说，我们利用Casimir操作员以及$ \ bar {e}（2）$组的发电机的换向关系。更重要的是，还提出了基于Schwinger的角动量振荡器模型的代数形式主义。讨论了$ \ bar {e}（2）$组及其对Landau级别堕落的影响的尺寸。
The planar Landau system which describes the quantum mechanical motion of a charged particle in a plane with a uniform magnetic field perpendicular to the plane, is explored within pedagogical settings aimed at the beginning graduate level. The system is known to possess the Euclidean symmetry in two dimensions with central extension $\bar{E}(2)$. In this paper, we revisit the well-known energy eigenvalues of the system, known as the Landau levels, by exploiting the related $\bar{e}(2)$ symmetry algebra. Specifically, we utilize the Casimir operator and the commutation relations of the generators of the $\bar{E}(2)$ group. More importantly, an algebraic formalism on this topic based on Schwinger's oscillator model of angular momentum is also presented. The dimensions of irreducible representations of the $\bar{E}(2)$ group and their implications on the degeneracy of Landau levels is discussed.
