On q-Deformed Supersymmetric Classical Mechanical Models

TL;DR

This paper generalizes supersymmetric classical mechanics by incorporating q-deformation using quantum groups and paragrassmann variables, specifically exploring the case where the deformation parameter is a cube root of unity.

Contribution

It introduces a novel q-deformed supersymmetric classical mechanics framework with paragrassmann variables and constructs related generators, derivatives, and actions.

Findings

Developed a q-deformed superspace with a paragrassmann variable satisfying  heta = 0.

Derived the generator and covariant derivative in the q-deformed setting.

Presented actions for possible superfields within this new framework.

Abstract

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