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arXiv · hep-th/9509098

Holomorphic Quantization on the Torus and Finite Quantum Mechanics

G. G. Athanasiu·E. G. Floratos·S. Nicolis
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Abstract

We construct explicitly the quantization of classical linear maps of $SL(2, R)$ 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 $SL(2, Z)$ to the subgroup $SL(2, Z)/Γ_l$, $Γ_l$ being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.

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G. G. Athanasiu, E. G. Floratos, S. Nicolis. 1996-11-10. Holomorphic Quantization on the Torus and Finite Quantum Mechanics. https://doi.org/10.1088/0305-4470%2F29%2F21%2F010

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