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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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GRAVITATIONAL ANOMALIES

GRAVITATIONAL ANOMALIES

Chapter:
(p.223) 10 GRAVITATIONAL ANOMALIES
Source:
Path Integrals and Quantum Anomalies
Author(s):

Kazuo Fujikawa

Hiroshi Suzuki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198529132.003.0010

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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