Anomalies and the Quantum Theory of Chiral Matter on a Line

Abstract

We review aspects of anomalies in quantum field theory, mainly the canonical quantization of anomalous gauge theories in two spacetime dimensions. This includes the unitary, Lorentz invariant quantization of the chiral Schwinger model; and quantization of nonabelian chiral bosons, described by a generalization of the Siegel action, away from “critical dimension”. Bosonization of chiral theories in background gauge and gravitational fields is extensively discussed via path integral methods.