$SU(1,1)$ covariant $s$-parametrized maps

• URL: http://arxiv.org/abs/2012.02993v1
• Date: Sat, 5 Dec 2020 10:02:56 GMT
• Title: $SU(1,1)$ covariant $s$-parametrized maps
• Authors: Andrei B. Klimov, Ulrich Seyfarth, Hubert de Guise, L. L. Sanchez-Soto
• Abstract summary: We propose a practical recipe to compute the $s$-parametrized maps for systems with $SU (1,1)$ symmetry. The particular case of the self-dual (Wigner) phase-space functions, defined on the upper sheet of the two-sheet hyperboloid are analyzed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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. 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 Poincar\'{e} disc) are analyzed.

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