Connection between two Wigner functions for spin systems

Centro de Ciencias Fi ´sicas, Universidad Nacional AutonomadeMexico, Apartado Postal 48-3, Cuernavaca, Morelos 62251, Mexico~Received 15 July 1999; published 10 February 2000!In 1981, Agarwal proposed a Wigner quasiprobability distribution function on the group SU~2! that servesto analyze two-particle spin states on a sphere. Recent work by our group has included the definition of anapparently distinct Wigner function on generic Lie groups whose natural range has the dimension of the groupand serves for all square-integrable representations; for the SO~3! case this entails a three-dimensional ‘‘meta-phase’’ space. Both have the fundamental properties covariance and completeness. Here we show how theformer is obtained as a restriction of the latter.PACS number~s!: 03.65.Bz, 42.50.FxI. CONSTRUCTION OF AGARWAL