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Intrepreting classical gauge theories

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/9780199287963.003.0004
Subject:
Philosophy, Philosophy of Science

This chapter presents and defends an interpretation of classical gauge theories, including electromagnetism. It argues that Yang-Mills gauge theories (but not general relativity) are best understood ... More


STRING THEORY AND GAUGE THEORY

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines the relationship between gauge theories and topological strings. A precise correspondence between string theory and gauge theory was formulated by 't Hooft (1974), who used as a ... More


Chern-Simons Theory, Matrix Models, and Topological Strings

Marcos Mariño

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string ... More


Classical gauge theories

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/9780199287963.003.0003
Subject:
Philosophy, Philosophy of Science

This chapter extends the analysis of classical gauge theories to encompass both non-Abelian Yang-Mills theories and the general theory of relativity. It explains what is meant by a non-Abelian ... More


Time and Structure in Canonical Gravity

Dean Rickles

in The Structural Foundations of Quantum Gravity

Published in print:
2006
Published Online:
October 2011
ISBN:
9780199269693
eISBN:
9780191699436
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199269693.003.0006
Subject:
Philosophy, Philosophy of Science

The interpretative problems of gauge theory take on what is arguably their most pathological form in the context of the problem of space (better known as the ‘hole argument’) and the problem of time. ... More


Quantized Yang–Mills gauge theories

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/9780199287963.003.0005
Subject:
Philosophy, Philosophy of Science

This chapter explains why physics could not rest content with classical Yang-Mills theories, and shows how a classical Yang-Mills field theory may be transformed into a quantum field theory. Quantum ... More


Quantum Gauge Theories

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.06
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The last few chapters have discussed many-boson theory and many-fermion theory because nature has many-boson systems and many-fermion systems. Do many-boson/many-fermion theories describe all the ... More


Loop representations

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/9780199287963.003.0007
Subject:
Philosophy, Philosophy of Science

This chapter explains the idea of a loop representation of a quantum field theory. Loop representations are important because they offer the prospect of a ‘gauge-free’ formulation of a gauge theory. ... More


Interpreting quantized Yang–Mills gauge theories

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/9780199287963.003.0008
Subject:
Philosophy, Philosophy of Science

This chapter begins the project of interpreting quantum gauge field theories. It rejects an interesting recent interpretation and explains why it is so difficult to arrive at a better one. The ... More


Mean-Field Theory of Spin Liquids and Quantum Order

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.09
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Topological order, as a generic phenomenon, not only appears in FQH systems, it can also appear in quantum spin systems. Quantum spin systems even allow the more general quantum order. This chapter ... 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


String Condensation—An Unification of Light and Fermions

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.10
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book has three types of theories: boson, fermion, and gauge theories. It asks which theories describe the elementary particles in our universe. Surprisingly, elementary particles are described ... More


QUANTUM BREAKING OF GAUGE SYMMETRY

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/9780198529132.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the quantum anomalies which appear in gauge symmetry itself. This class of anomalies generally appears in gauge theory, where both the vector and axial-vector couplings of ... More


Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Xiao-Gang Wen

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new ... 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


Weyl's “Purely Infinitesimal” Constitution of Field Physics

Thomas Ryckman

in The Reign of Relativity: Philosophy in Physics 1915-1925

Published in print:
2005
Published Online:
April 2005
ISBN:
9780195177176
eISBN:
9780199835324
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195177177.003.0006
Subject:
Philosophy, Philosophy of Science

It is shown how Weyl intertwined phenomenological analysis and mathematical construction in building the foundation of his “pure infinitesimal geometry” underlying gravitation and electromagnetism. ... More


 Gauge theories and fibre-bundle spaces

Frank Arntzenius

in Space, Time, and Stuff

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199696604
eISBN:
9780191738333
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199696604.003.0006
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

This chapter discusses the implications of gauge theories for our conception of properties, and for the reality of fibre-bundle spaces. One way of understanding such theories is to claim that the ... More


Mirror Symmetry, Hitchin's Equations, and Langlands Duality

Edward Witten

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter begins with a discussion of the A-model and B-model. It then describes mirror symmetry and Hitchin's equations, Hitchin fibration, ramification, wild ramification, and four-dimensional ... 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


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


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