Klimov, Andrei B.Seyfarth, Ulrichde Guise, HubertSánchez Soto, Luis Lorenzo2023-06-172023-06-172021-01-181751-811310.1088/1751-8121/abd7b4https://hdl.handle.net/20.500.14352/7820© 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).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.engjournal articlehttps://doi.org/10.1088/1751-8121/abd7b4https://iopscience.iop.orgopen access535Coherent statesQuantum-MechanicsRepresentationsQuantizationDynamicsSu(2)FormulationOperatorsÓptica (Física)2209.19 Óptica Física