Holomorphic quantization on the torus and finite quantum mechanics

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Abstract
We explicitly construct the quantization of classical linear maps of on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that finite quantum mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of to the subgroup , being the principal congruent subgroup , on a finite dimensional Hilbert space. The generators of the `rotation group' , , for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.

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