Quantum Deformation of the Poincare Supergroup and $\kappa$-deformed Superspace

TL;DR

This paper develops a quantum deformation of the N=1 superPoincaré group and superspace using a classical r-matrix, leading to a consistent $ ext{κ}$-deformation with potential implications for supersymmetric theories.

Contribution

It introduces a $ ext{κ}$-deformation of the superPoincaré group and superspace based on a classical r-matrix, extending quantum group methods to supersymmetry.

Findings

Constructed a graded Poisson structure for the superPoincaré group.

Derived a consistent quantum deformation with a fundamental mass parameter.

Discussed the dual $ ext{κ}$-deformed superspace and algebra.

Abstract

The classical $r$-matrix for $N=1$ superPoincar{\'e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{\'e} supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the superPoincar{\'e} group with the deformation parameter $q$ described by fundamental mass parameter $\kappa \quad (\kappa^{-1}=\ln{q})$. The $\kappa$-deformation of $N=1$ superspace as dual to the $\kappa$-deformed supersymmetry algebra is discussed.