Quadratic deformation of Minkowski space

TL;DR

This paper introduces a quadratic deformation of Minkowski space using twistors and quantum groups, explicitly computing the star product and its real forms, advancing the understanding of noncommutative spacetime structures.

Contribution

It presents a novel quadratic deformation of Minkowski space via twistors and quantum groups, with explicit star product calculations and real form analyses.

Findings

Explicit star product with quadratic Poisson bracket

Extension of the star product to differentiable functions

Determination of Euclidean and Minkowskian real forms

Abstract

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.