Algebraic Quantization on the Torus and Modular Invariance

Abstract

The aim of the Algebraic Quantization is the quantum description of a physical system by means of the unitary and irreducible representations of its symmetry group. Two cases have to be considered, corresponding to systems without constraints and to those with constraints, respectively. In the simplest case, the group e G of quantum symmetries will be a central extension by U(1) of the group G of classical symmetries.