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

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

2002-11-12

arxiv.org/abs/math-ph/0211019v1

Mod.Phys.Lett.A18:515-526,2003

Physics

Mathematical Physics

LaTeX 2e, amssym, 16 pages, no figure

Scientific paper

10.1142/S021773230300954X

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

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