Noninvariance Group for the Dirac Coulomb Problem

Abstract

All bound-state solutions of the Dirac Coulomb problem are shown to provide a Hilbert space for irreducible representations of the de Sitter group $O(4, 1)$ Selected solutions of this problem provide the basis for other representations of $O(4, 1)$ These results are compared to analogous results previously obtained for the Schrödinger Coulomb problem. Operator forms of the generators of $O(4, 1)$ are explicitly constructed as functions of p and r which operate on the Hilbert space provided by the Dirac problem.