COVARIANT AND CONSISTENT ANOMALIES IN 2 DIMENSIONS IN PATH-INTEGRAL FORMULATION

We give a definition of a one-parameter family of regularized chiral currents in a chiral non-Abelian gauge theory in two dimensions in path-integral formulation. We show that covariant and consistent currents are obtained from this family by selecting two specific values of the free parameter, and thus our regularization interpolates between these two. Our procedure uses chiral bases constructed from eigenfunctions of the same operator for defining psi(L) and psi(L)BAR. Definition of integration measure and regularization is done in terms of the same Hermitian operator D(alpha)BAR = partial derivativeBAR + ialphaABAR. Covariant and consistent currents (and indeed the entire family) are classically conserved. Difference with previous works are explained, in particular, that anomaly in a general basis does differ from the Jacobian contribution.