Chiral Anomaly and the Rational Quantization of the Hall Conductance

Abstract

The quantum Hall effect is shown be equivalent to a chiral anomaly in quantum electrodynamics. The integers ${n}_{1}$ and ${n}_{2}$ in the rationally quantized Hall conductance $g=(\frac{{e}^{2}}{2\ensuremath{\pi}\ensuremath{\hbar}})(\frac{{n}_{1}}{{n}_{2}})$ arise from vortex excitations carrying ${n}_{1}$ electrons and ${n}_{2}$ flux quanta. It is found that ${n}_{2}=2j$, where $j=l+\frac{1}{2}$ is the angular momentum per electron in the vortex. This explains the odd-denominator rule ${n}_{2}=2l+1$.