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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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QUANTUM BREAKING OF GAUGE SYMMETRY

QUANTUM BREAKING OF GAUGE SYMMETRY

Chapter:
(p.92) 6 QUANTUM BREAKING OF GAUGE SYMMETRY
Source:
Path Integrals and Quantum Anomalies
Author(s):

Kazuo Fujikawa

Hiroshi Suzuki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198529132.003.0006

This chapter discusses the quantum anomalies which appear in gauge symmetry itself. This class of anomalies generally appears in gauge theory, where both the vector and axial-vector couplings of gauge fields co-exist. As a special case, the chiral gauge theory where parity is broken is important in physical applications. The quantum breaking of gauge symmetry implies that the conservation of probability (unitarity) fails, and one cannot calculate higher-order quantum corrections in a consistent manner. The absence of the quantum anomaly in gauge symmetry is the basic requirement of consistent gauge theory, and the requirement imposes a stringent condition on the allowed lepton and quark multiplets in the Weinberg-Salam theory. In this connection, an interesting constraint called the integrability (or the Wess-Zumino consistency) condition appears. The actual evaluation of the covariant form of anomalies, which do not satisfy the integrability condition but have a gauge covariant form, is however much easier.

Keywords:   chiral gauge theory, unitarity, Weinberg-Salam theory, Wess-Zumino consistency, integrability condition, covariant

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