Path integrals and quantum anomalies / Kazuo Fujikawa and Hiroshi Suzuki.

Format:

Book

Author/Creator:

Fujikawa, K.

Contributor:

Suzuki, Hiroshi, 1964 January 7-

Series:

International series of monographs on physics (Oxford, England) ; 122.

Oxford science publications.

Oxford science publications

International series of monographs on physics ; no. 122

Standardized Title:

Keiro sekibun to taishōsei no ryōshiteki yabure. English

Language:

English

Subjects (All):

Path integrals.

Quantum field theory.

Physical Description:

1 online resource (297 p.)

Place of Publication:

Oxford : Clarendon Press ; New York : Published in the United States by Oxford University Press, 2004.

Language Note:

English

Summary:

The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. In this book, the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies.

Contents:

Contents; 1 Genesis of quantum anomalies; 1.1 Introduction; 1.2 Is the photon massless?; 1.3 The discovery of the quantum anomaly; 2 The Feynman path integral and Schwinger's action principle; 2.1 Quantum theory of a harmonic oscillator; 2.2 Path integral for the harmonic oscillator; 2.3 Quantization of a scalar field; 2.4 Path integral for fermions; 2.5 Path integral for Dirac particles; 2.6 Feynman path integral and Schwinger's action principle; 3 Quantum theory of photons and the phase operator; 3.1 Canonical quantization of the electromagnetic field

3.2 Path integral quantization of the electromagnetic field3.3 Photon phase operator and the notion of index; 3.4 Is there a hermitian phase operator?; 3.5 Index theorem for a harmonic oscillator; 4 Regularization of field theory and chiral anomalies; 4.1 Current conservation and Ward Takahashi identities; 4.2 Self-energy of the photon; 4.3 Quantum breaking of chiral symmetry; 4.4 Adler-Bardeen theorem; 5 The Jacobian in path integrals and quantum anomalies; 5.1 The chiral Jacobian in quantum electrodynamics; 5.2 Ward-Takahashi identities in quantum electrodynamics

5.3 Chiral anomaly in QCD-type theory5.4 Instantons; 5.5 Atiyah-Singer index theorem; 5.6 Nambu-Goldstone theorem; 6 Quantum breaking of gauge symmetry; 6.1 Gauge theory with axial-vector gauge fields; 6.2 Pauli-Villars regularization; 6.3 Chiral gauge theory and the quantum anomaly; 6.4 Covariant anomaly; 6.5 Anomaly cancellation in Weinberg-Salam theory; 6.6 The Wess-Zumino integrability condition; 6.7 Quantum anomalies and anomalous commutators; 7 The Weyl anomaly and renormalization group; 7.1 Scale transformation in field theory

7.2 Identities for the Weyl transformation and Weyl anomalies7.3 Identities related to coordinate transformations; 7.4 Weyl anomalies and β functions in QED and QCD; 7.5 The Weyl anomaly in curved space-time; 7.6 The Weyl anomaly in two-dimensional space-time; 7.7 Other applications of Weyl anomalies; 8 Two-dimensional field theory and bosonization; 8.1 Chiral anomalies in two-dimensional theory; 8.2 Abelian bosonization of fermions; 8.3 Non-Abelian bosonization of fermion theory; 8.4 Kac Moody algebra and Virasoro algebra; 8.5 Quantum theory of strings and Liouville action

8.6 Ghost number anomaly and the Riemann-Roch theorem9 Index theorem on the lattice and chiral anomalies; 9.1 Lattice gauge theory; 9.2 Lattice Dirac fields and species doubling; 9.3 Representation of the Ginsparg-Wilson algebra; 9.4 Atiyah-Singer index theorem on the lattice and the chiral anomaly; 9.5 The operator D satisfying the Ginsparg-Wilson relation; 9.6 Some characteristic features of lattice chiral theory; 10 Gravitational anomalies; 10.1 Chiral U(1) gravitational anomalies; 10.2 Evaluation by a quantum mechanical path integral; 10.3 Chern character and Dirac genus

10.4 Anomaly in general coordinate transformations

Notes:

Description based upon print version of record.

Description based on print version record.

Includes bibliographical references (p. 262-281) and index.

ISBN:

0-19-968670-X

1-280-75398-6

0-19-152381-X

9786610753987

1-4356-2081-X

OCLC:

271200975