Extended Fractional Supersymmetric Quantum Mechanics

Abstract

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the $F^{th}$ power of a conserved charge: $H=Q^F$ with $F=2,3,....$ This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable $\theta$ of order $F$, which satisfies ${\theta }^F=0$. 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. (To appear in "Mod.Phys.Lett.A")

12 pages, plain TEX, McGill/93-03

References in corpus (1)

• Fractional Supersymmetry and Quantum Mechanics

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