CURRENT COMMUTATOR ANOMALIES AND CHIRAL ANOMALIES IN THE CANONICAL FORMALISM

Without recourse to the Bjorken-Johnson-Low (BJL) method, current-current and current-electric-field commutator anomalies are evaluated in chiral gauge theories in two-and four-dimensional spacetime with the help of a gauge covariant regularization method. The results are consistent with previous analyses through the BJL method, and partially confirmed Faddeev’s conjecture on the commutator anomalies of the Gauss law constraint operators within the canonical formalism. The chiral anomalies of the current divergence are derived from these commutator anomalies in the Weyl gauge where current-electric-field commutator anomalies play important roles.