EXTENDED FRACTIONAL SUPERSYMMETRIC QUANTUM MECHANICS

Abstract

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the Fth power of a conserved charge: H=QF with F=2, 3,…. This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable θ of order F, which satisfies θF=0. Here, we present an alternative realization of such an algebra in which the internal space of the Hamiltonians is described by a tensor product of two paragrassmann variables of orders F and F−1 respectively. In particular, we find q-deformed relations (where q are roots of unity) between different conserved charges.