Unification of $\kappa$-Minkowski and extended Snyder spaces

TL;DR

This paper unifies $ppa$-Minkowski and extended Snyder noncommutative spaces by developing associative realizations, coproducts, star products, and twists, facilitating potential quantum field theory constructions on these geometries.

Contribution

It extends previous work on Snyder models to include a covariant $ppa$-Poincare9 realization, providing explicit algebraic structures in a Weyl-ordered form.

Findings

Derived coproduct, star product, and twist to first order in noncommutativity.

Unified framework for $ppa$-Minkowski and Snyder spaces.

Facilitates quantum field theory development on noncommutative geometries.

Abstract

In a recent paper, we have studied associative realizations of the noncommutative extended Snyder model, obtained by including the Lorentz generators (tensorial coordinates) and their conjugated momenta. In this paper, we extend this result to also incorporate a covariant realization of the $\kappa$-Poincar\'e spacetime. We obtain the coproduct, the associative star product and the twist in a Weyl-ordered realization, to first order in the noncommutativity parameters. This could help the construction of a quantum field theory based on this geometry.