Quantization of Gauge Theories with Anomalies

In this talk, we briefly review the basic concepts of anomalous gauge theories. It has been known for some time how theories with local anomalies can be handled. Recently it has been pointed out that global anomalies, which obstruct the quantization of certain gauge theories in the temporal gauge, get bypassed in canonical quantization. Anomalies of two different types can be involved in the quantization of gauge theories. The existence of divergence anomalies has been known for a long time [1]: certain classical theories have symmetry currents which cease to be conserved after quantization. In case the current is associated with a symmetry which is gauged, there appears to be a problem in the quantization of the theory because the equations of motion of the gauge fields require the current to be conserved. Fortunately, these apparently contradictory features – nonconservation due to the anomaly and conservation due to the gauging – can be ironed out because the anomaly itself can be made to vanish by going to a submanifold of the classical phase space before quantization. Of course, there is a difference from theories with nonanomalous gauge currents. In those theories, there is gauge freedom, which means that the theories can be described in any of an infinite variety of gauges. This is not possible in a straightforward manner in anomalous gauge theories, where the gauge is, as it were, fixed by the anomaly. However, we shall see below how an enlargement of the field content can lead to the usual kind of gauge freedom.