The Weyl-Wigner-Moyal formalism on a discrete phase space. I. A Wigner function for a nonrelativistic particle with spin

The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space L²\(mathbb{R}³\)otimes{mathcal{H}}^(s+1) and functions on the phase space mathbb{R}³timesmathbb{R}³times \{0,...,s\} times\{0,...,s\} is found. The expressions for the Stratonovich-Weyl quantizer, star product and Wigner functions of such systems for arbitrary values of spin are obtained in detail. As examples the Landau levels and the corresponding Wigner functions for a spin frac{1}{2} nonrelativistic particle as well as the magnetic resonance for a spin frac{1}{2} nonrelativistic uncharged particle are analysed.