The hidden symmetry of the Coulomb problem in relativistic quantum mechanics: From Pauli to Dirac

Additional conserved quantities associated with an extra symmetry govern a wide variety of physical systems ranging from planetary motion to atomic spectra. We give a simple derivation of the hidden symmetry operator for the Dirac equation in a Coulomb field and show that this operator may be reduced to the one introduced by Johnson and Lippmann to include the spin degrees of freedom. This operator has been rarely discussed in the literature and has been neglected in recent textbooks on relativistic quantum mechanics and quantum electrodynamics.