Canonical and Lie-algebraic twist deformations of Galilei algebra

TL;DR

This paper explores nonrelativistic limits of twisted Poincare algebras, resulting in five models of noncommutative space-times, including two novel Lie-algebraic deformations with mixed quantum and classical features.

Contribution

It introduces new Lie-algebraic nonrelativistic deformations of space-time, expanding the understanding of noncommutative geometries in nonrelativistic limits.

Findings

Five models of noncommutative nonrelativistic space-times derived.

Two new Lie-algebraic deformations with mixed quantum and classical properties.

Analysis of contraction-independent and contraction-dependent twist parameters.

Abstract

We describe various nonrelativistic contractions of two classes of twisted Poincare algebra: canonical one ($\theta_{\mu\nu}$-deformation) and the one leading to Lie-algebraic models of noncommutative space-times. The cases of contraction-independent and contraction-dependent twist parameters are considered. We obtain five models of noncommutative nonrelativistic space-times, in particular, two new Lie-algebraic nonrelativistic deformations of space-time, respectively, with quantum time/classical space and with quantum space/classical time.