相对论性量子力学中开普勒问题的隐对称性教学--从泡利到狄拉克电子
Teaching the hidden symmetry of the Kepler problem in relativistic quantum mechanics - from Pauli to Dirac electron
摘要：
库仑相互作用中的隐对称性是现代物理学的一个神秘问题。与超对称性相关的额外守恒量支配着各种各样的物理问题，从行星运动到原子光谱的精细和超精细结构。本文对库仑场中的狄拉克方程给出了相对论性量子力学中隐对称算符的一个简单推导。我们建立了这个算子可以减少到一个介绍约翰逊和李普曼。值得注意的是，这个算符在文献中很少讨论，因此物理学家们并不熟悉，甚至在最近的相对论量子力学和/或量子电动力学教科书中也被省略了。
英文摘要：
Hidden symmetry in Coulomb interaction is one of the mysterious problems of modern physics. Additional conserved quantities associated with extra symmetry govern wide variety of physics problems, from planetary motion till fine and hyperfine structures of atomic spectra. In this paper we present a simple derivation of hidden symmetry operator in relativistic quantum mechanics for the Dirac equation in the Coulomb field. We established that this operator may be reduced to the one introduced by Johnson and Lippmann. It is worthwhile to notice that this operator was discussed in literature very rarely and so is not known well among physicists and was omitted even in the recent textbooks on relativistic quantum mechanics and/or quantum electrodynamics.
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