On q-Deformed Supersymmetric Classical Mechanical Models

Abstract

Based on the idea of quantum groups and paragrassmann variables, we presenta generalization of supersymmetric classical mechanics with a deformation parameter $q= \exp{\frac{2 πi}{k}}$ dealing with the $k =3$ case. The coordinates of the $q$-superspace are a commuting parameter $t$ and a paragrassmann variable $θ$, where $% θ^3 = 0$. The generator and covariant derivative are obtained, as well as the action for some possible superfields.