Derivation of chiral anomalies and commutator anomalies in a fixed-time regularization method

Abstract

A gauge-covariant regularization method is introduced to evaluate current-current and current--electric-field commutator anomalies in chiral gauge theories in two- and four-dimensional spacetime within the Hamiltonian formalism. The results are consistent with those obtained by the Bjorken-Johnson-Low method. Provided that the electric fields commute with each other, a covariant expression is found for the commutator anomaly of the Gauss-law operator. The regularized current is shown to have the covariant anomaly in its divergence due to its noncommutativity with the electric field.