Minimal bosonization of double-graded supersymmetric quantum mechanics

• URL: http://arxiv.org/abs/2108.06243v3
• Date: Tue, 16 Nov 2021 15:31:51 GMT
• Title: Minimal bosonization of double-graded supersymmetric quantum mechanics
• Authors: C. Quesne
• Abstract summary: The superalgebra of $Z2$-graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. The central element $Z$ has the property of distinguishing between degenerate eigenstates of the Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The superalgebra of $\Z_2^2$-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 $\Z_2$-graded superalgebra in the framework of a Calogero-Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the $\Z_2^2$-graded superalgebra, the central element $Z$ has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

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