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Modern Physics Letters A

CURVATURE OF HILBERT SPACE AND q-DEFORMED 'QUANTUM MECHANICS'

Binayak Dutta-Roy, Gautam Kumar Ghosh

Published May 20, 1993• 1 citation
Publisher

Abstract

A role for the parameter q in deformed algebras is sought in the context of the geometry of the Hilbert space.
DOI
10.1142/s0217732393001148

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Fractional supersymmetric quantum mechanics of order λ is realized in terms of the generators of a generalized deformed oscillator algebra and a ℤλ-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 ℤλ-graded uniform topological symmetry of type (1, 1, …, 1) with topological invariants generalizing the Witten index.
Fractional supersymmetric quantum mechanics of order λ is realized in terms of the generators of a generalized deformed oscillator algebra and a Zλgrading 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 Zλ-graded uniform topological symmetry of type (1, 1,..., 1) with topological invariants generalizing the Witten index.