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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:

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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