We prove that the Wigner–Stratonovich–Agarwal operator that defines the quasi-probability distribution on the sphere [for the SU(2) dynamical group] can be written as an integral of the SU(2) (irreducible unitary) representation element with respect to a single variable that labels the orbits in the coadjoint representation. This allows us to consider contractions of the SU(2) quasi-probability distribution to the cases of the Heisenberg–Weyl group and the two-dimensional Euclidean group.
© 2000 Optical Society of America
(000.1600) General : Classical and quantum physics
Original Manuscript: June 7, 2000
Revised Manuscript: August 28, 2000
Manuscript Accepted: June 28, 2000
Published: December 1, 2000
A. B. Klimov and S. M. Chumakov, "Quasi-probability distributions for the simplest dynamical groups," J. Opt. Soc. Am. A 17, 2315-2318 (2000)