Extended Fractional Supersymmetric Quantum Mechanics

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the F th power of a conserved charge: H = Q 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 θ = 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. ∗ E-mail address: [email protected]