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Para, pseudo, and orthosupersymmetric quantum mechanics and their bosonization

C. Quesne
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Abstract

We consider the problem of bosonizing supersymmetric quantum mechanics (SSQM) and some of its variants, i.e., of realizing them in terms of only boson-like operators without fermion-like ones. In the SSQM case, this is realized in terms of the generators of the Calogero-Vasiliev algebra (also termed deformed Heisenberg algebra with reflection). In that of the SSQM variants, this is done by considering generalizations of the latter algebra, namely the $C_λ$-extended oscillator algebras, where $C_λ$ is the cyclic group of order~$λ$.

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C. Quesne. 2000-12-15. Para, pseudo, and orthosupersymmetric quantum mechanics and their bosonization. https://arxiv.org/abs/math-ph/0012033

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