The Weyl-Wigner-Moyal formalism for spin

The Weyl-Wigner-Moyal formalism is developed for spin by means of a correspondence between spherical harmonics and spherical-harmonic tensor operators. The exact asymptotic relation among the P, Q, and Weyl symbols is found, and the analogue of the Moyal expansion is developed for the Weyl symbol of the product of two operators in terms of the symbols for the individual operators. It is shown that in the classical limit, the Weyl symbol for a commutator equals i times the Poisson bracket of the corresponding Weyl symbols.