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Anomalies in Quantum Field Theory$
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Reinhold A. Bertlmann

Print publication date: 2000

Print ISBN-13: 9780198507628

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780198507628.001.0001

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Path integral and anomaly

Path integral and anomaly

(p.249) 5 Path integral and anomaly
Anomalies in Quantum Field Theory

Reinhold A. Bertlmann

Oxford University Press

Chapter 4 presented a thorough investigation of the anomaly within perturbation theory. This chapter presents the nonperturbative view. Section 5.1 performs a chiral transformation of the path integral and finds the anomalous Ward identity. Section 5.2 regularizes the transformation Jacobian à la Fujikawa, and in this way derives the singlet anomaly; the two-dimensional case is added in Section 5.3. Section 5.4 shows the regularization independence of the anomaly and Section 5.5 discusses the conflict between gauge- and chiral symmetry in the light of an uncertainty principle. Section 5.6 demonstrates the generalization of the path integral method to non-Abelian fields leading to non-Abelian anomaly. Finally, Section 5.7 carries out the regularization of the Jacobian by means of the heat kernel method and by the zeta function procedure.

Keywords:   path integrals, Ward identity, Jacobian, gauge symmetry, chiral symmetry, non-Abelian anomaly, heat kernel method, zeta function

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