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Minimal bosonization of double-graded supersymmetric quantum mechanics

C. Quesne·2021

Abstract

The superalgebra of ₂²-graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired by a description of the corresponding ₂-graded superalgebra in the framework of a Calogero-Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the ₂²-graded superalgebra, the central element Z has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

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