SU(1,1) covariant s-parametrized maps



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Klimov, Andrei B. and Seyfarth, Ulrich and de Guise, Hubert and Sánchez Soto, Luis Lorenzo (2021) SU(1,1) covariant s-parametrized maps. Journal of physics. A, Mathematical and theoretical, 54 (6). ISSN 1751-8113

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We propose a practical recipe to compute the s-parametrized maps for systems with SU(1, 1) symmetry using a connection between the Q- and P-symbols through the action of an operator invariant under the group. This establishes equivalence relations between s-parametrized SU(1, 1)-covariant maps. The particular case of the self-dual (Wigner) phase-space functions, defined on the upper sheet of the two-sheet hyperboloid (or, equivalently, inside the Poincare disc) are analysed.

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© 2021 IOP Publishing Ltd.
We dedicate this work to the memory of Prof. David J Rowe, of the University of Toronto. The work of ABK is partially supported by the Grant 254127 of CONACyT (Mexico); HdG is supported in part by NSERC of Canada, LLSS is supported by the Spanish Ministerio de Ciencia e Innovacion (Grant PGC2018-099183-B-I00).

Uncontrolled Keywords:Coherent states; Quantum-Mechanics; Representations; Quantization; Dynamics; Su(2); Formulation; Operators
Subjects:Sciences > Physics > Optics
ID Code:64049
Deposited On:19 Feb 2021 16:39
Last Modified:29 Apr 2022 15:42

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