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.

Noncommutative spacetime symmetries from covariant quantum mechanics / Moia, Alessandro. - In: ADVANCES IN HIGH ENERGY PHYSICS (ONLINE). - ISSN 1687-7365. - ELETTRONICO. - 2017:(2017). [10.1155/2017/4042314]

Noncommutative spacetime symmetries from covariant quantum mechanics

Alessandro Moia
2017

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.
2017
Deformed relativistic symmetries; noncommutative spacetime; covariant quantum mechanics; quantum-gravity phenomenology
01 Pubblicazione su rivista::01a Articolo in rivista
Noncommutative spacetime symmetries from covariant quantum mechanics / Moia, Alessandro. - In: ADVANCES IN HIGH ENERGY PHYSICS (ONLINE). - ISSN 1687-7365. - ELETTRONICO. - 2017:(2017). [10.1155/2017/4042314]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1125441
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