Fractional Superspace Formulation of Generalized Mechanics

Abstract

Supersymmetric (pseudo-classical) mechanics has recently been generalized to {\it fractional}\/ supersymmetric mechanics. In such a construction, the action is invariant under fractional supersymmetry transformations, which are the $F^{\,\rm th}$ roots of time translations (with $F=1,2,...$). Associated with these symmetries, there are conserved charges with fractional canonical dimension $1+1/F$. Using \pg\ variables satisfying $\t^F=0$, we present a fractional-superspace formulation of this construction.