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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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(p.451) 12 Gravitation
Anomalies in Quantum Field Theory

Reinhold A. Bertlmann

Oxford University Press

This chapter focuses on gravitation. It first reviews some basic concepts of the Riemannian geometry and establishes notation. It then discusses the gravitational action, specifically the fermionic action. It introduces Einstein-, Lorentz-, and Weyl anomalies by violating the corresponding Einstein-, Lorentz-, and Weyl symmetries, and establishes consistency conditions. The equivalence of the Einstein- and Lorentz anomaly is demonstrated, and the covariant anomaly is discussed. Finally, the chapter treats gravitation on a BRS level, deriving the SZ chain of descent equations. Index theorems are use to carry out explicit anomaly examples.

Keywords:   gravitation, Riemannian geometry, fermionic action, Einstein anomaly, Lorentz anomaly, Weyl anomaly

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