Exact supersymmetry in the relativistic hydrogen atom in general dimensions—supercharge and the generalized Johnson-Lippmann operator

Abstract

A Dirac particle in general dimensions moving in a 1∕r potential is shown to have an exact supersymmetry, for which the two supercharge operators are obtained in terms of (a D-dimensional generalization of) the Johnson-Lippmann operator, an extension of the Runge-Lenz-Pauli vector that relativistically incorporates spin degrees of freedom. So the extra symmetry (S(2)) in the quantum Kepler problem, which determines the degeneracy of the levels, is so robust as to accommodate the relativistic case in arbitrary dimensions.