The operator structures for the constants of the motion of the relativistic hydrogen atom are examined. ThoughJ 3 andJ · J are constants of the motion,J is not. Its replacement, $\tilde {\rm K}$ , is shown to emerge rather naturally in transforming the equation to spherical coordinates. The separation of variables is presented in hypercomplex number form. This leads to some interesting suggestions regarding the matter/antimatter operator for the Dirac equation.