## 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