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Kappa-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations

Meljanac, Daniel; Meljanac, Stjepan; Mignemi, Salvatore; Štrajn, Rina (2019) Kappa-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations. Physical Review D, 99 . ISSN 2470-0010

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We consider kappa-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincaré algebra is unaltered, while the other is a general extension where the Poincaré algebra is deformed. As an example we fix the Jordanian twist and the corresponding realization of noncommutative coordinates, coproduct of momenta, and addition of momenta. An extension with a one-parameter family of realizations of the Lorentz generators, dilatation and momenta closing the Poincaré-Weyl algebra is considered. The corresponding physical interpretation depends on the way the Lorentz algebra is implemented in phase space. We show how the spectrum of the relativistic hydrogen atom depends on the realization of the generators of the Poincaré-Weyl algebra.

Item Type: Article
Uncontrolled Keywords: noncommutative geometry ; Jordanian twist ; algebra: Lorentz ; Poincare-Weyl ; phase space ; dispersion relation
Subjects: NATURAL SCIENCES > Physics
Divisions: Division of Materials Physics
Theoretical Physics Division
Depositing User: Daniel Meljanac
Date Deposited: 23 Jul 2019 13:42
DOI: 10.1103/PhysRevD.99.126012

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