The classical basis for $\kappa$-deformed Poincar\'e (super)algebra and the second $\kappa$-deformed supersymmetric Casimir

TL;DR

This paper derives explicit formulas for generators of the eformed Poincare9 (super)algebra in terms of classical generators, revealing a new eformation of the supersymmetric Casimir operator with quantum deformation only in the coalgebra sector.

Contribution

It provides the first explicit formulas for eformed Poincare9 (super)algebra generators as functions of classical generators and introduces a novel eformation of the supersymmetric Casimir.

Findings

Explicit formulas for eformed generators in terms of classical ones.

New eformation of the supersymmetric Casimir operator.

Quantum deformation present only in the coalgebra sector.

Abstract

We present here the general solution describing generators of \kdef \poin algebra as the functions of classical \poin algebra generators as well as the inverse formulae. Further we present analogous relations for the generators of N=1 D=4 \kdef \poin superalgebra expressed by the classical \poin superalgebra generators. In such a way we obtain the \kdef \poin (super)algebras with all the quantum deformation present only in the coalgebra sector. Using the classical basis of \kdef \poin superalgebra we obtain as a new result the $\k$-deformation of supersymmetric covariant spin square Casimir.