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Path Integrals and Quantum Anomalies$
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Kazuo Fujikawa and Hiroshi Suzuki

Print publication date: 2004

Print ISBN-13: 9780198529132

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198529132.001.0001

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REGULARIZATION OF FIELD THEORY AND CHIRAL ANOMALIES

REGULARIZATION OF FIELD THEORY AND CHIRAL ANOMALIES

Chapter:
(p.47) 4 REGULARIZATION OF FIELD THEORY AND CHIRAL ANOMALIES
Source:
Path Integrals and Quantum Anomalies
Author(s):

Kazuo Fujikawa

Hiroshi Suzuki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198529132.003.0004

This chapter illustrates the regularization of field theory by taking quantum electrodynamics (QED) as an example, showing that the mass of the photon remains at 0 even after higher-order quantum corrections. The simplest example of the quantum breaking of chiral symmetry is also explained. The one-loop fermionic diagrams become fundamental in these considerations, and the gauge covariant regularization of one-loop Feynman diagrams for arbitrary theory is explained. It is shown that the chiral anomaly is defined independently of Feynman diagrams in perturbation theory. The basic idea of the Adler-Bardeen theorem, which asserts that identity with the chiral anomaly does not receive any higher-order corrections, is briefly discussed.

Keywords:   quantum electrodynamics, QED, chiral symmetry, gauge covariant regularization, chiral anomaly, Feynman diagrams, perturbation theory, Adler-Bardeen theorem

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