  A novel realization of the classical SU(2) algebra is introduced for the
Dirac relativistic hydrogen atom defining a set of operators that, besides,
allow the factorization 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 the Dirac equation using algebraic methods. To acomplish this, a similar
path to the one used in the angular momentum case is employed; hence, the
radial eigenfuntions calculated comprise non unitary representations of the
algebra. One of the interesting properties of such non unitary representations
is that they are not labeled by integer nor by half-integer numbers as happens
in the usual angular momentum representation.
