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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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INDEX THEOREM ON THE LATTICE AND CHIRAL ANOMALIES

INDEX THEOREM ON THE LATTICE AND CHIRAL ANOMALIES

Chapter:
(p.196) 9 INDEX THEOREM ON THE LATTICE AND CHIRAL ANOMALIES
Source:
Path Integrals and Quantum Anomalies
Author(s):

Kazuo Fujikawa

Hiroshi Suzuki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198529132.003.0009

Recent progress in the treatment of Dirac fields in lattice gauge theory has allowed the chiral symmetry and associated anomaly on the lattice to be discussed in a manner similar to that in continuum theory. In particular, the index theorem on the lattice can be discussed. The analysis of the index theorem on the discrete lattice itself has certain subtle aspects, but lattice theory deals with completely regularized quantities, and thus some of the subtle aspects in continuum theory are now given a more rigorous basis. It is explained that all the results of chiral anomalies in continuum theory are reproduced in a suitable continuum limit of lattice gauge theory, providing a uniform and consistent treatment of both continuum and lattice theories.

Keywords:   Dirac field, lattice gauge theory, chiral anomaly, continuum theory, continuum limit

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