Connection between two Wigner functions for spin systems - art. no. 034101

In 1981, Agarwal proposed a Wigner quasiprobability distribution function o n the group SU(2) that serves to analyze two-particle spin states on a sphe re. Recent work by our group has included the definition of an apparently d istinct Wigner function on generic Lie groups whose natural range has the d imension;of the group and serves for all square-integrable representations; for the SO(3) case this entails a three-dimensional "metaphase" space; Bot h have the fundamental properties covariance and completeness. Here we show how the former is obtained as a restriction of the latter.