Anomalous but consistent chiral schwinger model

Abstract

We showed that anomalous CSM can be quantized consistently in spite of the anomaly with the bosonized lagrangian. If we use equation of motion for the gauge field, then the anomalous divergence for the current vanishes. The gauge variation on the lagrangian also vanishes by virtue of the equation of motion for Ao. Consistency can be also shown explicitly by studying fermionic lagrangian. Some authors in the gauge invariant formulation with the Wess-Zumino action and we have known that gauge noninvariant formulation of CSM is nothing but a specific gauge of the gauge invariant formulation. This also explains why anomalous CSM is consistently quantized.