Noncommutative spacetime symmetries from covariant quantum mechanics
arXiv:1707.05407 · doi:10.1155/2017/4042314
Abstract
In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates. However, spacetime noncommutativity can also be introduced into single-particle covariant quantum mechanics, replacing the commuting operators representing the particle's spacetime coordinates with noncommuting ones. In this paper we provide a full characterization of a wide class of physically sensible single-particle noncommutative spacetime models and the associated deformed relativistic symmetries. In particular, we prove that they can all be obtained from the standard Minkowski model and the usual Poincaré transformations via a suitable change of variables. Contrary to previous studies, we find that spacetime noncommutativity does not affect the dispersion relation of a relativistic quantum particle, but only the transformation properties of its spacetime coordinates under translations and Lorentz transformations.
arXiv comment14 pages; v2: minor changes to match published version
References in corpus (12)
- Quantum Field Theory on Noncommutative Spaces
- Bicrossproduct structure of -Poincare group and non-commutative geometry
- Quantum Spacetime Phenomenology
- On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
- The principle of relative locality
- 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
- Spacetime states and covariant quantum theory
- Noncommutative Spaces and Poincaré Symmetry
- Relative locality in a quantum spacetime and the pregeometry of -Minkowski
- Dual redshift on Planck-scale-curved momentum spaces
- First results of the Noether theorem for Hopf-algebra spacetime symmetries
- Predictive description of Planck-scale-induced spacetime fuzziness