Noncommutative Spacetime Symmetries from Covariant Quantum Mechanics

In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinaryMinkowski 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 awide 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 fromthe standardMinkowskimodel and the usual Poincar'e 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.