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Gauge invariance and gauge fixing

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/9780198787754.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 11 is the first of four chapters that discuss various issues connected with the Standard Model of fundamental interactions at the microscopic scale. It discusses the important notion of gauge ... More


Abelian Gauge Theories

JEAN ZINN-JUSTIN

in Quantum Field Theory and Critical Phenomena

Published in print:
2002
Published Online:
January 2010
ISBN:
9780198509233
eISBN:
9780191708732
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509233.003.0018
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on abelian gauge theory, whose physical realization is Quantum Electrodynamics (QED). The chapter is organized as follows. It begins with elementary considerations about the ... More


Geometry and Quantum Dynamics

Laurent Baulieu, John Iliopoulos, and Roland Sénéor

in From Classical to Quantum Fields

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198788393
eISBN:
9780191830310
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788393.003.0014
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills ... More


Green’s functions and the dynamical action principle

JAGDISH MEHRA and KIMBALL A. MILTON

in Climbing the Mountain: The Scientific Biography of Julian Schwinger

Published in print:
2003
Published Online:
February 2010
ISBN:
9780198527459
eISBN:
9780191709593
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527459.003.0009
Subject:
Physics, History of Physics

In a remarkable lecture Julian Schwinger delivered at the University of Nottingham on July 14, 1993, on the occasion of his receiving an honorary degree, entitled ‘The Greening of quantum field ... More


Kinetic Equations

Nikolai B. Kopnin

in Theory of Nonequilibrium Superconductivity

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198507888
eISBN:
9780191709722
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507888.003.10
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter derives the kinetic equations for the two-component distribution function in a gauge-invariant form. The collision integrals for interaction of excitations with impurities, phonons, and ... More


Relational Blockworld and Quantum Field Theory

Michael Silberstein, W.M. Stuckey, and Timothy McDevitt

in Beyond the Dynamical Universe: Unifying Block Universe Physics and Time as Experienced

Published in print:
2018
Published Online:
March 2018
ISBN:
9780198807087
eISBN:
9780191844850
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198807087.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics, History of Physics

A brief introduction to particle physics and quantum field theory (QFT) is presented in the main thread of chapter 5. The impasse of unification in particle physics is historically reviewed, showing ... More


The electromagnetic potentials

J. Pierrus

in Solved Problems in Classical Electromagnetism: Analytical and Numerical Solutions with Comments

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198821915
eISBN:
9780191861055
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198821915.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

This chapter expresses the fields E(r, t) and B(r, t) in terms of the electromagnetic potentials Ф(r, t) and A(r, t), and shows that these potentials are defined only up to a gauge transformation. ... More


A rough guide to quantum electrodynamics

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/9780199699322.003.0040
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Arguably the most important achievement of quantum field theory is quantum electrodynamics (QED), which describes the interaction between electrons and photons, and this theory is presented in ... More


The free field

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0032
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter studies the structure of Maxwell’s equations in a vacuum and the action from which they are derived, while emphasizing the consequences of their gauge invariance. Gauge invariance, on ... More


The Maxwell equations

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0030
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies ... 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


Duality in generalized Ising models

Franz J. Wegner

in Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School: Volume 103, August 2014

Published in print:
2017
Published Online:
March 2017
ISBN:
9780198785781
eISBN:
9780191827600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198785781.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

These lecture notes deal with Ising models with interactions containing products of more than two spins. After a number of examples have been given, some general statements are presented. Of ... 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


The Hamiltonian formalism

Steven Carlip

in General Relativity: A Concise Introduction

Published in print:
2019
Published Online:
March 2019
ISBN:
9780198822158
eISBN:
9780191861215
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822158.003.0012
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

So far, general relativity has been viewed from the four-dimensional Lagrangian perspective. This chapter introduces the (3+1)-dimensional Hamiltonian formalism, starting with the ADM form of the ... More


Field-Dependent Transport

Klaus Morawetz

in Interacting Systems far from Equilibrium: Quantum Kinetic Theory

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198797241
eISBN:
9780191838743
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797241.003.0020
Subject:
Physics, Condensed Matter Physics / Materials

Using a gauge-invariant formulation of Green’s function, the electric-field dependent kinetic equations are derived in Born and RPA (dynamically screened) approximation. The feedback and ... More


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