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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:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

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:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

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


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