Weyl–Heisenberg covariant quantization for the discrete torus

Covariant integral quantization is implemented for systems whose phase space is [Formula: see text], i.e. for systems moving on the discrete periodic set [Formula: see text] mod [Formula: see text]. The symmetry group of this phase space is the periodic discrete version of the Weyl–Heisenberg group, namely the central extension of the abelian group [Formula: see text]. In this regard, the phase space is viewed as the left coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on [Formula: see text], is square integrable on the phase We derive the corresponding covariant integral quantizations from (weight) functions on the phase space, and display their phase space portrait.