Relation between the Chiral Anomaly and the Quantized Hall Effect

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Abstract
A simple method is used to calculate the currents induced by static uniform electromagnetic fields in the ground state of a two-dimensional electron gas. This is done for both the relativistic and the nonrelativistic cases. This analysis is used to explain the apparent similarity between the anomalous vacuum current in three-dimensional quantum electrodynamics and the quantized Hall current. The different natures of the two currents are demonstrated, and it is shown that the effective action for the gauge field in the nonrelativistic case does not contain a genuine Chern-Simons term. This precludes any attempt to use the chiral anomaly to explain the quantized Hall effect.