## The empirical import of gauge symmetry

*Richard Healey*

### in Gauging What's Real: The Conceptual Foundations of Gauge Theories

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199287963
- eISBN:
- 9780191713453
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199287963.003.0006
- Subject:
- Philosophy, Philosophy of Science

This chapter argues that gauge symmetry is a purely formal feature of our theoretical representations with no empirical consequences. It distinguishes theoretical symmetries of a theory from ... More

## Breaking Symmetries

*Gian Francesco Giudice*

### in A Zeptospace Odyssey: A Journey into the Physics of the LHC

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199581917
- eISBN:
- 9780191723001
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199581917.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Symmetries play a fundamental role in modern physics. This chapter introduces this concept by discussing the meaning of symmetries in mathematics and in physics, explaining the significance of Lie ... More

## Symmetries III: Global symmetries in field theory

*Anthony Duncan*

### in The Conceptual Framework of Quantum Field Theory

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199573264
- eISBN:
- 9780191743313
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573264.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter examines the role of global symmetries in local quantum field theories. It shows that exact global symmetries are rare — indeed, if we take gravitational effects into account, probably ... More

## THE JACOBIAN IN PATH INTEGRALS AND 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/9780198529132.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter gives a general path integral formulation of the quantum anomaly for chiral symmetry. The quantum anomaly is identified as the Jacobian arising from the symmetry transformation of path ... More

## Effective Field Theory with Nambu–Goldstone Modes

*Antonio Pich*

### in Effective Field Theory in Particle Physics and Cosmology: Lecture Notes of the Les Houches Summer School: Volume 108, July 2017

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780198855743
- eISBN:
- 9780191889370
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198855743.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

These lectures provide an introduction to the low-energy dynamics of Nambu–Goldstone fields, which associated with some spontaneous (or dynamical) symmetry breaking, using the powerful methods of ... More

## O(N) vector model in the ordered phase: Goldstone modes

*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/9780198787754.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 10 examines the case of the spontaneous breaking of a continuous symmetry. When there is spontaneous symmetry breaking, the correlation length diverges at all temperatures in the ordered ... More

## The Higgs boson: A major discovery and a problem

*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/9780198787754.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 12 describes the main steps in the construction of the electroweak component of the Standard Model of particle physics. The classical Abelian Landau–Ginzburg–Higgs mechanism is recalled, ... More

## Chiral Symmetry

*Michael E. Peskin*

### in Concepts of Elementary Particle Physics

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198812180
- eISBN:
- 9780191850301
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198812180.003.0014
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter introduces chiral symmetry, the extra symmetry that QCD acquires when the masses of quarks are set to zero. It introduces the concept of spontaneous symmetry breaking and explains the ... More

## Broken symmetry

*Tom Lancaster and Stephen J. Blundell*

### in Quantum Field Theory for the Gifted Amateur

- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0027
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

An important concept is symmetry breaking and this is treated here. This idea is introduced in the context of phase transitions and the chapter also shows how to describe symmetry breaking with a ... More

## The Cantabrigian

*Andrew Zangwill*

### in A Mind Over Matter: Philip Anderson and the Physics of the Very Many

- Published in print:
- 2021
- Published Online:
- January 2021
- ISBN:
- 9780198869108
- eISBN:
- 9780191905599
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198869108.003.0010
- Subject:
- Physics, History of Physics

Anderson spends a sabbatical year at the University of Cambridge. He informs graduate student Brian Josephson about spontaneous symmetry breaking in superconductors and Josephson discovers the ... More

## Water, Water, Here and There

*Steven E. Vigdor*

### in Signatures of the Artist: The Vital Imperfections That Make Our Universe Habitable

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198814825
- eISBN:
- 9780191852954
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198814825.003.0004
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Chapter 4 deals with the stability of the proton, hence of hydrogen, and how to reconcile that stability with the baryon number nonconservation (or baryon conservation) needed to establish a ... More

## Symmetries and symmetry breaking

*Michael Kachelriess*

### in Quantum Fields: From the Hubble to the Planck Scale

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198802877
- eISBN:
- 9780191841330
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802877.003.0013
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The spontaneous breaking of symmetries (SSB) is discussed for global symmetries and Goldstones theorem is derived. The renormalisation of theories with SSB is studied using the effective potential. ... More

## Gauge Theories with Spontaneous Symmetry Breaking

*Michael E. Peskin*

### in Concepts of Elementary Particle Physics

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198812180
- eISBN:
- 9780191850301
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198812180.003.0016
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter describes theories that combine the ideas of gauge symmetry and spontaneous symmetry breaking. It explains that this combination gives rise to massive spin-1 bosons. This construction is ... More

## Breaking Symmetry

*Andrew Zangwill*

### in A Mind Over Matter: Philip Anderson and the Physics of the Very Many

- Published in print:
- 2021
- Published Online:
- January 2021
- ISBN:
- 9780198869108
- eISBN:
- 9780191905599
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198869108.003.0006
- Subject:
- Physics, History of Physics

The postwar Red Scare and McCarthyism solidified Anderson’s left-of-center politics. He solidified his position at Bell Labs by using the concept of superexchange to explain neutron scattering data ... More

## The Higgs boson

*G. Barr, R. Devenish, R. Walczak, and T. Weidberg*

### in Particle Physics in the LHC Era

- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198748557
- eISBN:
- 9780191811203
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198748557.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter starts with a simple introduction to gauge invariance and spontaneous symmetry breaking. An elementary introduction to Lagrangians in classical and quantum mechanics is given. A ... More

## Classical fields in curved spacetime

*Iosif L. Buchbinder and Ilya L. Shapiro*

### in Introduction to Quantum Field Theory with Applications to Quantum Gravity

- Published in print:
- 2021
- Published Online:
- April 2021
- ISBN:
- 9780198838319
- eISBN:
- 9780191874666
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198838319.003.0012
- Subject:

This chapter discusses classical fields in an arbitrary Riemann spacetime. General considerations are followed by the formulation of scalar fields with non-minimal coupling. Spontaneous symmetry ... More

## Gross–Neveu–Yukawa and Gross–Neveu models

*Jean Zinn-Justin*

### in Quantum Field Theory and Critical Phenomena: Fifth Edition

- Published in print:
- 2021
- Published Online:
- June 2021
- ISBN:
- 9780198834625
- eISBN:
- 9780191872723
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198834625.003.0020
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter, a model is considered that can be defined in continuous dimensions, the Gross– Neveu–Yukawa (GNY) model, which involves N Dirac fermions and one scalar field. The model has a ... More

## The “Higgs” Boson, and its Field in the “Vacuum”

*Alvaro De Rújula*

### in Enjoy Our Universe: You Have No Other Choice

- Published in print:
- 2018
- Published Online:
- February 2020
- ISBN:
- 9780198817802
- eISBN:
- 9780191859366
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198817802.003.0022
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Spontaneous symmetry breaking. The symmetric Higgs bottle and its asymmetric state of lowest energy. The “expectation value” of the Higgs field in the vacuum. Why and how the vacuum is not void, it ... More

## From Classical to Quantum Fields

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.001.0001
- Subject:

Quantum field theory has become the universal language of most modern theoretical physics. This book is meant to provide an introduction to this subject with particular emphasis on the physics of the ... More

## The Standard Model (SM) of fundamental interactions

*Jean Zinn-Justin*

### in Quantum Field Theory and Critical Phenomena: Fifth Edition

- Published in print:
- 2021
- Published Online:
- June 2021
- ISBN:
- 9780198834625
- eISBN:
- 9780191872723
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198834625.003.0023
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The Standard Model (SM) 2020 of weak, electromagnetic and strong interactions, based on gauge symmetry and spontaneous symmetry breaking, describes all known fundamental interactions at the ... More