Suppression of local degrees of freedom of gauge fields by chiral anomalies

A path-integral quantization is presented for the chiral Schwinger model on a Riemann surface. Gauge invariance is maintained by integrating over all gauge potentials without the usual gauge fixing. All local degrees of freedom of the gauge field are suppressed after the integration of the anomalous effective action over a gauge orbit. The resulting theory is a topological one for the surviving global gauge excitations. The general implications for consistent quantization of chiral gauge theories are also discussed.