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

Abstract

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 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 1/2 nonrelativistic particle as well as the magnetic resonance for a spin 1/2 nonrelativistic uncharged particle are analysed.

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