Supersymmetry and superalgebra for the two-body system with a Dirac oscillator interaction

Abstract

Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac oscillator in its one- and many-body versions has had a great number of applications. Recently, it included the analytic expression for the eigenstates and eigenvalues of a two-particle system with a new type of Dirac oscillator interaction of frequency~$ω$. By considering the latter together with its partner corresponding to the replacement of~$ω$ by~$-ω$, we are able to get a supersymmetric formulation of the problem and find the superalgebra that explains its degeneracy.