库仑势与Witten超代数
Coulomb Potential and Witten Superalgebra
摘要：
在经典力学和量子力学中对库仑-开普勒问题的附加隐藏对称性进行了评述。主要目的是阐明这种对称性在简化物理问题中的作用，展示光谱推导的代数可能性。并给出了原始结果。它们是狄拉克方程中隐藏的对称性，其中证明了狄拉克哈密顿量在某种威滕超代数下的不变性要求，仅挑选出库仑势。在任意高维的问题也被认为是。在N=2的超对称性背景下，传统的库仑势观点将被改变
英文摘要：
The additional hidden symmetry of the Coulomb-Kepler problem is reviewed in classical as well as in quantum mechanics. The main purpose is to elucidate the role of this kind of symmetries in the reduction of physical problems, to show algebraic possibilities of derivation of spectra. The original results are presented also. They are hidden symmetries in the Dirac equation, where it is shown that the requirement of invariance of the Dirac Hamiltonian under some kind of Witten's superalgebra, picks out the Coulomb potential only. The problem in the arbitrary higher dimensions is also considered. It is derived that the traditional view on the Coulomb potential is to be changed in the context of N=2 supersymmetry
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