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

TL;DR

This paper develops a supersymmetric framework for a two-particle Dirac oscillator system, revealing its superalgebra structure and explaining its degeneracy, building on previous single-particle and many-body studies.

Contribution

It introduces a supersymmetric formulation for a two-particle Dirac oscillator with a new interaction, deriving the superalgebra that accounts for its degeneracy.

Findings

Derived the eigenstates and eigenvalues for the two-particle system.

Established the superalgebra structure underlying the degeneracy.

Connected the supersymmetric approach to previous single-particle models.

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~$\omega$. By considering the latter together with its partner corresponding to the replacement of~$\omega$ by~$-\omega$, we are able to get a supersymmetric formulation of the problem and find the superalgebra that explains its degeneracy.