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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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Path Integrals and Quantum Anomalies

Kazuo Fujikawa

Hiroshi Suzuki

Oxford University Press

This chapter discusses chiral anomalies associated with the gravitational field, namely, gravitational anomalies. It discusses gravitational generalization of chiral U(1) anomalies for ordinary gauge fields. A method for evaluating the Dirac genus and Chern characters in general 2n-dimensional Euclidean space-time is given. It is explained that there appear to be quantum anomalies in general coordinate and local Lorentz transformations for chiral Dirac fields in (4n+2)-dimensional curved space-time. If these anomalies are not cancelled, the basic principles of general relativity and quantum theory become incompatible with each other.

Keywords:   gravitational field, chiral U(1) anomaly, Dirac genus, Chern character, general coordinate transformation, local Lorentz transformation, curved space-time, general relativity

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