Nonunitary representations of the SU(2) algebra in the Dirac equation witha Coulomb potential

A novel realization of the classical SU(2) algebra is introduced for the Di rac relativistic hydrogen atom defining a set of operators that allow the f actorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve th e Dirac equation using algebraic methods. A similar path to the one used in the angular momentum case is used; hence, the radial eigenfunctions so cal culated comprise nonunitary representations of the algebra. One of the inte resting properties of such nonunitary representations is that they are not labeled by integer nor by half-integer numbers, as occurs in the usual angu lar momentum representation. (C) 1999 American Institute of Physics. [S0022 -2488(99)02004-6].