Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio’s oscillator

Abstract

The Dirac hydrogen atom with spin symmetry is shown and has a SO(4) symmetry. The generators are derived, and the corresponding Casimir operator leads to the energy spectrum naturally. This type of hydrogen atom is connected to a four-dimensional Dirac system with equal scalar and vector harmonic oscillator potential by the Kustaanheimo-Stiefel transformation with a constraint.