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 Poincar disc) are analysed.

中文翻译：

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SU（1，1）协变量s参数化映射

我们提出了一个实用的配方，通过组中算子不变式的作用，使用Q符号和P符号之间的连接来计算具有SU（1，1）对称性的系统的s参数映射。这在s参数化的SU（1，1）-协变量映射之间建立了等价关系。分析了在两层双曲面的上层（或等效地在Poincar盘内部）定义的自对偶（维格纳）相空间函数的特殊情况。