Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential

Abstract

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.

arXiv comment20 pages 1 eps figure in a single zipped file, submitted to J. Math. Phys

References in corpus (2)

• Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics
• New non-unitary representations in a Dirac hydrogen atom

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