论文标题
Landau问题中的物理对称性和量规选择
Physical symmetries and gauge choices in the Landau problem
论文作者
论文摘要
由于Landau问题的特殊性质，其中磁场均匀地扩散在整个二维平面上，因此必须存在三个保守的数量，即两个保守的动量和一个保守的电子轨道角动量，独立于计量势的选择。因此，可以通过将Landau Hamiltonian以及上述三个保守的操作员之一对角线来获得Landau问题的量子本征函数，结果可以将Landau问题的量子机械特征函数写下来，以供任意规格潜力。本文的目的是基于该规范独立的配方阐明仪表选择的含义，并特别意图揭示了在最近在核子自旋分解问题上提倡的规范轨道角度动量的规范轨道角度动量概念的物理意义。最后，我们的分析显示出仪表对称性的物理上空的侧面。
Due to a special nature of the Landau problem, in which the magnetic field is uniformly spreading over the whole two-dimensional plane, there necessarily exist three conserved quantities, i.e. two conserved momenta and one conserved orbital angular momentum for the electron, independently of the choice of the gauge potential. Accordingly, the quantum eigen-functions of the Landau problem can be obtained by diagonalizing the Landau Hamiltonian together with one of the above three conserved operators with the result that the quantum mechanical eigen-functions of the Landau problem can be written down for arbitrary gauge potential. The purpose of the present paper is to clarify the meaning of gauge choice in the Landau problem based on this gauge-potential-independent formulation, with a particular intention of unraveling the physical significance of the concept of gauge-invariant-extension of the canonical orbital angular momentum advocated in recent literature on the nucleon spin decomposition problem. At the end, our analysis is shown to disclose a physically vacuous side face of the gauge symmetry.
