Fractional Superspace Formulation of Generalized Mechanics

TL;DR

This paper introduces a fractional superspace formulation for generalized mechanics, extending supersymmetric mechanics to include fractional supersymmetry transformations that are roots of time translations, with associated conserved charges.

Contribution

It presents a novel fractional superspace framework for fractional supersymmetric mechanics using exttt{ extbackslash pg} variables satisfying exttt{ extbackslash t extasciF}^F=0, expanding the mathematical structure of supersymmetry.

Findings

Developed a fractional superspace formulation for fractional supersymmetric mechanics.

Defined exttt{ extbackslash pg} variables satisfying exttt{ extbackslash t extasciF}=0.

Connected fractional supersymmetry transformations to conserved charges with fractional canonical dimension.

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.