On a Full Quantization of the Torus

TL;DR

This paper presents a full quantization of the torus that fully represents classical observables without the Groenewold-Van Hove obstruction, demonstrating a complete and irreducible quantum representation.

Contribution

It introduces a prequantization of the torus that achieves a full quantization with an irreducible representation of classical observables, overcoming known quantization obstructions.

Findings

Complete set of classical observables is irreducibly represented.

No Groenewold-Van Hove obstruction in this quantization.

Provides a model for full quantization of the torus.

Abstract

I exhibit a prequantization of the torus which is actually a ``full'' quantization in the sense that a certain complete set of classical observables is irreducibly represented. Thus in this instance there is no Groenewold-Van Hove obstruction to quantization.