Kinetic normal ordering and the Hamiltonian structure of U(1) chiral anomalies in 3 + 1 dimensions

Abstract

We present a fixed-time Hamiltonian derivation of the U(1) chiral anomaly equation and the anomalous commutators of the vector and axial currents in 3 + 1 dimensions. Our computation is based on the physically correct normal ordering with respect to kinetic energy and shows that the only regularizations involved in the derivation of the chiral anomaly are kinetic normal ordering and a point-splitting regularization of the current operators. We obtain the standard results for the anomaly equation and the anomalous commutator [ j 0, j 5 0]; however, we obtain non-anomalous commutators for [ j 0, j 5 i ] and [ j i , j 5 0], in contrast to the BJL results.