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CONCLUDING REMARKS

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers a possible intuitive explanation of quantum breaking of symmetries as well as the subjects which are not discussed in the main chapters, such as the descent formula for gauge ... More


Anomalies in Quantum Field Theory

Reinhold A. Bertlmann

Published in print:
2000
Published Online:
February 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper ... More


Trajectories of Neurobehavioral Development: The Clinical Neuroscience of Child Abuse

Carryl P. Navalta, Akemi Tomoda, and Martin H. Teicher

in Stress, Trauma, and Children's Memory Development: Neurobiological, cognitive, clinical and legal perspectives

Published in print:
2008
Published Online:
May 2008
ISBN:
9780195308457
eISBN:
9780199867387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195308457.003.0003
Subject:
Psychology, Developmental Psychology

This chapter reviews what is known about the clinical neuroscience of child abuse and provides new findings on neuroanatomical effects of child abuse and their relation with memory processes. ... More


Constructions: Descriptive Factors

Ronald W. Langacker

in Cognitive Grammar: A Basic Introduction

Published in print:
2008
Published Online:
May 2008
ISBN:
9780195331967
eISBN:
9780199868209
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195331967.003.0007
Subject:
Linguistics, Syntax and Morphology

Constructions are characterized in terms of four basic factors: correspondences, profiling, elaboration, and constituency. Correspondences are the basis for semantic and grammatical integration; they ... More


TWO-DIMENSIONAL FIELD THEORY AND BOSONIZATION

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the quantum anomalies in two-dimensional field theory. Two-dimensional field theory is important in connection with conformal field theory and its applications to string theory ... More


Gravitation

Reinhold A. Bertlmann

in Anomalies in Quantum Field Theory

Published in print:
2000
Published Online:
February 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


Introduction

Reinhold A. Bertlmann

in Anomalies in Quantum Field Theory

Published in print:
2000
Published Online:
February 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This introductory chapter begins with a historical background of the anomalies discussed in this book, axial- or the chiral anomaly corresponding to an axial- or chiral fermion current. It then ... More


SEIBERG DUALITY FOR SUSY QCD

John Terning

in Modern Supersymmetry: Dynamics and Duality

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567639
eISBN:
9780191718243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567639.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter begins with a discussion of the phases of gauge theories. It then discusses the moduli space for F = N, IR fixed points, Seiberg's nontrivial solution to the 't Hooft anomaly matching, ... More


Chern–Simons form, homotopy operator and anomaly

Reinhold A. Bertlmann

in Anomalies in Quantum Field Theory

Published in print:
2000
Published Online:
February 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The Chern–Simons form and the homotopy operator plays an important role in connection with anomalies. In fact, the anomaly can be calculated on pure algebraic grounds from a variation of the ... More


Stora–Zumino chain of descent equations

Reinhold A. Bertlmann

in Anomalies in Quantum Field Theory

Published in print:
2000
Published Online:
February 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter shows how the singlet anomaly in 2n dimensions determines the non-Abelian anomaly in (2n - 2) dimensions via a set of equations. These are part of a whole chain of equations, which ... More


NONPERTURBATIVE RESULTS

John Terning

in Modern Supersymmetry: Dynamics and Duality

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567639
eISBN:
9780191718243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567639.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The previous chapter showed that in order to understand SUSY breaking, nonperturbative SUSY theories need to be studied. Progress in this area requires an understanding of some standard ... More


Quantum anomalies: A few physics applications

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0017
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 17 exhibits various examples where classical symmetries cannot be transferred to quantum theories. The obstructions are characterized by anomalies. The examples involve chiral symmetries ... More


DOS AND TUNNELING

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

The chapter starts with a discussion of the density of states renormalization in the normal state of a superconductor caused by fluctuation pairing which occurs close to the transition temperature. ... More


GRAVITATIONAL ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


GENESIS OF QUANTUM ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the history of quantum anomalies. The original indication of the anomaly appeared immediately after the modern formulation of field theory, namely, renormalization theory. ... More


REGULARIZATION OF FIELD THEORY AND CHIRAL ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter illustrates the regularization of field theory by taking quantum electrodynamics (QED) as an example, showing that the mass of the photon remains at 0 even after higher-order quantum ... More


INDEX THEOREM ON THE LATTICE AND CHIRAL ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

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 ... More


From Random Walks to Random Matrices

Jean Zinn-Justin

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models ... More


Unitary groups

Adam M. Bincer

in Lie Groups and Lie Algebras: A Physicist's Perspective

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199662920
eISBN:
9780191745492
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662920.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Unitary groups are defined. An explicit choice of generators in the defining representation is displayed and used to abstract commutation relations for u(n). It is shown that the center of U(n) has ... More


Category Mistakes

Ofra Magidor

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199572977
eISBN:
9780191758942
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199572977.001.0001
Subject:
Philosophy, Philosophy of Language, Metaphysics/Epistemology

Category mistakes are sentences such as ‘Green ideas sleep furiously’ or ‘The theory of relativity is eating breakfast’. Such sentences strike most speakers as highly infelicitous, and the main aim ... More


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