Noether analysis of the twisted Hopf symmetries of canonical noncommutative spacetimes

We study the twisted Hopf-algebra symmetries of observer-independent canonical spacetime noncommutativity, for which the commutators of the spacetime coordinates take the form [x̂μ,x̂ν]=iθμν with observer-independent (and coordinate-independent) θμν. 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 κ-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. © 2008 The American Physical Society