• Open Access

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

D. Meljanac, S. Meljanac, S. Mignemi, and R. Štrajn
Phys. Rev. D 99, 126012 – Published 19 June 2019

Abstract

We consider κ-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.

  • Received 19 April 2019

DOI:https://doi.org/10.1103/PhysRevD.99.126012

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

D. Meljanac1,*, S. Meljanac2,†, S. Mignemi3,4,‡, and R. Štrajn5,§

  • 1Division of Materials Physics, Ruđer Bošković Institute, Bijenička cesta 54, 10002 Zagreb, Croatia
  • 2Division of Theoretical Physics, Ruđer Bošković Institute, Bijenička cesta 54, 10002 Zagreb, Croatia
  • 3Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari, Italy
  • 4INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato, Italy
  • 5Department of Electrical Engineering and Computing, University of Dubrovnik, Ćira Carića 4, 20000 Dubrovnik, Croatia

  • *Daniel.Meljanac@irb.hr
  • meljanac@irb.hr
  • smignemi@unica.it
  • §rina.strajn@unidu.hr

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Issue

Vol. 99, Iss. 12 — 15 June 2019

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