Chiral anomalies and Poincaré invariance ∗

I consider theories of Dirac fermions with different regularizations, leading to different chiral anomalies. I have investigated the Poincaré invariance properties of these theories. I find that both Lorentz and translational invariance are anomalously violated in general, but that they are respected in a theory that is regularized to give a Wess-Zumino consistent anomaly (the Bardeen anomaly). In a theory that is regularized to give a covariant anomaly, Poincaré invariance is not respected, and in this case I calculate the divergence of the angular momentum current and energy-momentum tensor in a nonabelian theory with external vector and axial vector sources. PACS numbers: 11.30.Rd; 11.30.Cp