Covariant and consistent anomalies in two 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 thesame operator for defining _L and. Definition of integration measure and regularization is done in terms of thesame Hermitian operator. 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.