Constrained quantization in algebraic field theory

TL;DR

This paper explores the quantization of classical gauge theories with constraints in algebraic quantum field theory, using symplectic reduction and Rieffel induction to analyze gauge symmetries, anomalies, and theta angles.

Contribution

It introduces a novel approach linking symplectic reduction and Rieffel induction to study gauge symmetries and anomalies in algebraic quantum field theory.

Findings

Provides a framework for analyzing gauge anomalies algebraically

Connects classical and quantum gauge theories through constrained quantization

Offers insights into theta angles within algebraic quantum field theory

Abstract

Quantization relates Poisson algebras to $C^*$-algebras. The analysis of local gauge symmetries in algebraic quantum field theory is approached through the quantization of classical gauge theories, regarded as constrained dynamical systems. This approach is based on the analogy between symplectic reduction and Rieffel induction on the classical and on the quantum side, respectively. Thus one is led to a description of e.g. $\theta$-angles and gauge anomalies in the algebraic setting.