Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-05-25
Phys.Lett. B312 (1993) 115-120
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, plain TEX, McGill/92-54, to appear in Phys. Lett. B (minor corrections and references updated)
Scientific paper
10.1016/0370-2693(93)90496-5
We present a set of quantum-mechanical Hamiltonians which can be written as the $F^{\,\rm th}$ power of a conserved charge: $H=Q^F$ with $[H,Q]=0$ and $F=2,3,...\, .$ This new construction, which we call {\it fractional}\/ supersymmetric quantum mechanics, is realized in terms of \pg\ variables satisfying $\t^F=0$. Furthermore, in a pseudo-classical context, we describe {\it fractional}\/ supersymmetry transformations as the $F^{\,\rm th}$ roots of time translations, and provide an action invariant under such transformations.
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