Noncommutative Lightcones from Quantum SO(2,1) Conformal Groups

TL;DR

This paper introduces five new noncommutative lightcones in 2+1 dimensions, derived from quantum deformations of the SO(2,1) conformal group, with analysis of their covariance, classification, and geometric properties.

Contribution

It presents novel noncommutative lightcones as quantizations of Poisson structures, expanding the understanding of quantum conformal geometries in 2+1 dimensions.

Findings

Five new noncommutative lightcones constructed

Covariance under quantum SO(2,1) deformations established

Localization properties linked to geometric features

Abstract

Five new families of noncommutative lightcones in 2+1 dimensions are presented as the quantizations of the inequivalent Poisson homogeneous structures that emerge when the lightcone is constructed as a homogeneous space of the SO(2,1) conformal group. Each of these noncommutative lightcones maintains covariance under the action of the respective quantum deformation of the SO(2,1) conformal group. We discuss the role played by SO(2,1) automorphisms in the classification of inequivalent Poisson homogeneous lightcones, as well as the geometric aspects of this construction. The localization properties of the novel quantum lightcones are analyzed and shown to be deeply connected with the geometric features of the Poisson homogeneous spaces.