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We study the Weyl-Wigner transform in the case of discrete variables definedin a Hilbert space of finite prime-number dimensionality $N$. We define afamily of Weyl-Wigner transforms as function of a phase parameter. We show thatit is only for a specific value of the parameter that all the properties wehave examined have a parallel with the case of continuous variables defined inan infinite-dimensional Hilbert space. A geometrical interpretation is brieflydiscussed.

A Family of Weyl-Wigner Transforms for Discrete Variables Defined in a Finite-Dimensional Hilbert Space