Anomalous Chiral Action from the Path-Integral

Details Anomalous Chiral Action from the Path-Integral Anomalous Chiral Action from the Path-Integral

1996-02-26

arxiv.org/abs/hep-th/9602137v1

Int.J.Mod.Phys. A13 (1998) 523-551

Physics

High Energy Physics

High Energy Physics - Theory

28 pages

Scientific paper

10.1142/S0217751X98000226

By generalizing the Fujikawa approach, we show in the path-integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern-Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. Our method uses Schwinger's ``proper-time'' representation of the Green's function and the gauge invariant point-splitting technique. We find that the consistency requirement and the point-splitting technique allow both an anomalous and a non-anomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory, or, a non-anomalous theory

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