  We show that the Pauli-Villars regularized action for a scalar field in a
gravitational background in 1+1 dimensions has, for any value of the cutoff M,
a symmetry which involves non-local transformations of the regulator field plus
(local) Weyl transformations of the metric tensor. These transformations, an
extension to the regularized action of the usual Weyl symmetry transformations
of the classical action, lead to a new interpretation of the conformal anomaly
in terms of the (non-anomalous) Jacobian for this symmetry. Moreover, the
Jacobian is automatically regularized, and yields the correct result when the
masses of the regulators tend to infinity. In this limit the transformations,
which are non-local in a scale of 1/M, become the usual Weyl transformation of
the metric. We also present the example of the chiral anomaly in 1+1
dimensions.
