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(R3)⊗H(s+1) and functions on the phase space R3×R3×{0,…,s}×{0,…,s} is found. The expressions for the Stratonovich‐Weyl quantiser, 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 12 nonrelativistic particle as well as the magnetic resonance for a spin 12 nonrelativistic uncharged particle are analysed. 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(R3)⊗H(s+1) and functions on the phase space R3×R3×{0,…,s}×{0,…,s} is found. The expressions for the Stratonovich‐Weyl quantiser, 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 12 nonrelativistic particle as well as the magnetic resonance for a spin 12 nonrelativistic uncharged particle are analysed.