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Fractional supersymmetric quantum mechanics, topological invariants and generalized deformed oscillator algebras

C. Quesne
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Abstract

Fractional supersymmetric quantum mechanics of order $λ$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_λ$-grading structure is imposed on the Fock space of the latter. This realization is shown to be fully reducible with the irreducible components providing $λ$ sets of minimally bosonized operators corresponding to both unbroken and broken cases. It also furnishes some examples of Z$_λ$-graded uniform topological symmetry of type (1, 1, ..., 1) with topological invariants generalizing the Witten index.

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C. Quesne. 2002-11-12. Fractional supersymmetric quantum mechanics, topological invariants and generalized deformed oscillator algebras. https://doi.org/10.1142/s021773230300954x

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