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arXiv · hep-th/9510006

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

M. Moshinsky·C. Quesne·Yu. F. Smirnov
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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.

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M. Moshinsky, C. Quesne, Yu. F. Smirnov. 1995-10-03. Supersymmetry and superalgebra for the two-body system with a Dirac oscillator interaction. https://doi.org/10.1088/0305-4470%2F28%2F22%2F020

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