Constrained quantization in algebraic field theory

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.