New non-unitary representations in a Dirac hydrogen atom

TL;DR

This paper introduces novel non-unitary SU(2) representations for the Dirac hydrogen atom, enabling an algebraic solution of bound states without requiring integer or half-integer quantum labels.

Contribution

It presents new non-unitary SU(2) representations and an algebraic method to solve the Dirac hydrogen atom problem, expanding the mathematical framework used.

Findings

Successfully spans the bound state eigenstates algebraically.

Requires an extra phase to close the algebra.

Does not depend on integer or half-integer quantum labels.

Abstract

New non-unitary representations of the SU(2) algebra are introduced for the case of the Dirac equation with a Coulomb potential; an extra phase, needed to close the algebra, is also introduced. The new representations does not require integer or half integer labels. The set of operators defined are used to span the complete space of bound state eigenstates of the problem thus solving it in an essentially algebraic way.