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 and functions on the phase space 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 nonrelativistic particle as well as the magnetic resonance for a spin nonrelativistic uncharged particle are analysed.

中文翻译：

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离散相空间上的Weyl-Wigner-Moyal形式主义。I.具有自旋的非相对论粒子的维格纳函数

提出了具有离散内部自由度的量子粒子的Weyl-Wigner-Moyal形式主义。发现希尔伯特空间中的算子与相空间中的函数之间的一一对应关系。详细获得了此类系统对于任意旋转值的Stratonovich-Weyl量化器，星积和Wigner函数的表达式。作为示例，分析了自旋非相对论粒子的朗道能级和相应的维格纳函数以及自旋非相对论不带电粒子的磁共振。