Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 022, 20 pages      arXiv:2112.12038      https://doi.org/10.3842/SIGMA.2022.022

Deformed Quantum Phase Spaces, Realizations, Star Products and Twists

Stjepan Meljanac a and Rina Štrajn b
a) Division of Theoretical Physics, Ruder Bovšković Institute, Bijenička cesta 54, 10002 Zagreb, Croatia
b) Department of Electrical Engineering and Computing, University of Dubrovnik, Ćira Carića 4, 20000 Dubrovnik, Croatia

Received December 27, 2021, in final form March 14, 2022; Published online March 23, 2022

Abstract
We review deformed quantum phase spaces and their realizations in terms of undeformed phase space. In particular, methods of calculation for the star product, coproduct of momenta and twist from realizations are presented, as well as their properties and the relations between them. Lie deformed quantum phase spaces and Snyder type spaces are considered. Examples of linear realizations of the $\kappa$-Minkowski spacetime are elaborated. Finally, some new results on quadratic deformations of quantum phase spaces and a generalization of Yang and triply special relativity models are presented.

Key words: deformed quantum phase spaces; realizations; star products; twists.

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