Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its   connection with Ginocchio's oscillator
  The Dirac hydrogen atom with spin symmetry is shown has a SO(4) symmetry. The generators are derived, and the corresponding Casimir operator leads to the energy spectrum naturally. This type 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. 
Fu-Lin Zhang, Bo Fu, Jing-Ling Chen