Algebraic Quantization on the Torus and Modular Invariance

TL;DR

This paper explores algebraic quantization on the torus, highlighting how modular invariance emerges as a subgroup of good operators, and discusses topological features like fractional quantum numbers and anomalies.

Contribution

It introduces a framework for algebraic quantization on groups, demonstrating the natural appearance of modular invariance on the torus and its relation to topological phenomena.

Findings

Modular invariance appears as a subgroup of good operators.

The framework describes fractional quantum numbers and topological anomalies.

New features of systems with non-trivial topology are characterized algebraically.

Abstract

New features of systems with non-trivial topology such as fractional quantum numbers, inequivalent quantizations, good operators, topological anomalies, etc. are described in the framework of an algebraic quantization procedure on a group. Modular invariance naturally appears as a subgroup of good operators in the particular case of the torus.