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 $L^2({\mathbb{R}}^3)\otimes {\mathcal{H}}^{(s+1)}$ and functions on the phase space ${\mathbb{R}}^3\times {\mathbb{R}}^3\times \{0,...,s\}\times \{0,...,s\}$ 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.

34 pages. New references have been added. Some comments have been included. The title has been modified

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• Reconstruction of non-classical cavity field states with snapshots of their decoherence
• Quantum gravity and the Coulomb potential
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Cited by in corpus (2)

• The geometrical interpretation of the photon position operator
• The Weyl -- Wigner -- Moyal Formalism on a Discrete Phase Space. II. The Photon Wigner Function