Chiral anomalies and Poincare invariance

Details Chiral anomalies and Poincare invariance Chiral anomalies and Poincare invariance

1999-12-11

arxiv.org/abs/hep-th/9912095v2

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, revised version, two references added

Scientific paper

I study variations of the fermionic determinant for a nonabelian Dirac fermion with external vector and axial vector sources. I consider different regularizations, leading to different chiral anomalies when the variations are chiral transformations. For these different regularizations, I then consider variations associated with Poincare transformations. I find that both Lorentz and translational invariance are anomalously violated in general, but that they are respected when the variations of the determinant are regularized to give a Wess-Zumino consistent anomaly (the Bardeen anomaly). If the variations are regularized to give a covariant anomaly, then Poincare invariance is not respected. Following Manohar in an investigation of Poincare anomalies in a chiral gauge theory, this gives an alternative way to understand the need for a consistent regularization of the variations of the fermionic determinant.

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