Twisted Hopf symmetries of canonical noncommutative spacetimes and the no-pure-boost principle

TL;DR

This paper investigates the twisted-Hopf algebra symmetries of canonical noncommutative spacetimes, revealing the necessity of nontrivial transformation parameters and demonstrating that all symmetries include translations, with results independent of ordering conventions.

Contribution

It introduces a consistent framework for analyzing symmetries in canonical noncommutative spacetimes using twisted Hopf algebras, including nontrivial transformation parameters.

Findings

Symmetries require nontrivial commutators between parameters and coordinates.

All symmetry transformations include a translation component.

Conserved charges are independent of Weyl map choices.

Abstract

We study the twisted-Hopf-algebra symmetries of observer-independent canonical spacetime noncommutativity, for which the commutators of the spacetime coordinates take the form [x^{mu},x^{nu}]=i theta^{mu nu} with observer-independent (and coordinate-independent) theta^{mu nu}. We find that it is necessary to introduce nontrivial commutators between transformation parameters and spacetime coordinates, and that the form of these commutators implies that all symmetry transformations must include a translation component. We show that with our noncommutative transformation parameters the Noether analysis of the symmetries is straightforward, and we compare our canonical-noncommutativity results with the structure of the conserved charges and the "no-pure-boost" requirement derived in a previous study of kappa-Minkowski noncommutativity. We also verify that, while at intermediate stages of the analysis we do find terms that depend on the ordering convention adopted in setting up the Weyl map, the final result for the conserved charges is reassuringly independent of the choice of Weyl map and (the corresponding choice of) star product.