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

摘要

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) with topological invariants generalizing the Witten index. [References: 43]