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

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.

arXiv comment12 pages

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• Planck-scale effects on Bose-Einstein condensates
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• Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
• Trapped Bose-Einstein condensates with Planck-scale induced deformation of the energy-momentum dispersion relation
• Strongest atomic physics bounds on Non-Commutative Quantum Gravity Models
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• Classical Group Field Theory
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• Lifetime of flying particles in canonical Doubly Special Relativity
• Total momentum and other Noether charges for particles interacting in a quantum spacetime
• On the distance observable in the Moyal plane and in a novel two-dimensional space with string-theory pregeometry
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• The Lorentz Group, Noncommutative Space-Time, and Nonlinear Electrodynamics in Majorana-Oppenheimer Formalism