Nonlocal parity transformations and anomalies

We present an alternative derivation of the parity anomaly for a massless D irac field in 2 + 1 dimensions coupled to a gauge field. The anomaly functi onal, a Chern-Simons action for the gauge field, is obtained from the nontr ivial Jacobian corresponding to a nonlocal symmetry of the Pauli-Villars re gularized action. That Jacobian is well-defined, finite, and yields the sta ndard Chern-Simons term when the cutoff tends to infinity. (C) 2000 Elsevie r Science B.V. All rights reserved.