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The Link Invariants of the Chern-Simons Field Theory : New Developments in Topological Quantum Field Theory - Enore Guadagnini

The Link Invariants of the Chern-Simons Field Theory

New Developments in Topological Quantum Field Theory

Hardcover Published: 1st August 1993
ISBN: 9783110140286
Number Of Pages: 326
For Ages: 22+ years old

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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject.

Editorial Board

Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Honorary Editor

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Titles in planning include

Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2018)
Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, Botjan Gabrovek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Introduction
Quantum physics and classical electromagnetismp. 1
Abelian Chern-Simons actionp. 5
Non-Abelian Chern-Simons actionp. 6
Basic notions of knot theory
Ambient and regular isotopyp. 10
Link invariantsp. 14
Framing and satellitesp. 18
Framing in field theory
Abelian Chern-Simons theoryp. 23
Framed Wilson line operatorsp. 25
Non-Abelian Chern-Simons theory
Covariant quantizationp. 31
One-loop effective actionp. 34
Higher order resultsp. 39
Observables and perturbation theory
Wilson line operatorsp. 42
Perturbative computationsp. 44
Properties of the expectation values
Holonomy matrixp. 47
Discrete symmetriesp. 49
Satellite formulaep. 50
Ordering fermions and knot observables
Ordering fermionsp. 58
Antiperiodic boundary conditionsp. 60
Knot observablesp. 64
Braid group
Artin braid groupp. 66
Hecke algebrap. 69
R-matrix and braids
Quantum group approachp. 74
Lie algebras and monodromy representationsp. 79
Quasi-Hopf algebrap. 80
Chern-Simons monodromies
Schrodinger picturep. 83
Universality of the link invariantsp. 87
The inexistent shiftp. 90
Defining relations
Calculus rulesp. 92
The extended Jones polynomial
The values of the unknotsp. 102
Hopf linkp. 108
Trefoil knotp. 110
Figure-eight knotp. 112
Connection with the Jones polynomialp. 118
Bracket connectionp. 120
Reconstruction theoremsp. 122
General properties
Twist variablep. 127
Recovered field theoryp. 130
Links in a solid torusp. 133
Satellitesp. 138
Skein relationp. 141
Projectorsp. 145
Borromean ringsp. 147
Connected sumsp. 153
Mutationsp. 156
Unitary groups
Fundamental skein relationp. 161
Casimir operatorp. 164
Composite statesp. 168
Pattern linksp. 172
Higher dimensional representationsp. 176
Polynomial structurep. 179
SU(3) examplesp. 181
Reduced tensor algebra
The restated solutionp. 187
Outlookp. 190
Representation ringp. 192
The three-spherep. 195
Reduced tensor algebrap. 196
Roots of unityp. 201
Special casesp. 204
Surgery on three-manifolds
Mapping class group of the torusp. 208
Solid torip. 209
Dehn surgeryp. 214
Links in three-manifoldsp. 217
Elementary surgeriesp. 220
Physical interpretationp. 222
The fundamental groupp. 224
Surgery and field theory
Basic pairingp. 228
Properties of the Hopf matrixp. 231
Elementary surgery operatorsp. 237
Surgery operatorp. 243
Surgery rules and Kirby movesp. 246
Observables in three-manifolds
The manifold S[superscript 2] x S[superscript 1]p. 249
The manifold RP[superscript 3]p. 258
Lens spacesp. 262
The Poincare manifoldp. 266
The manifold T[superscript 2] x S[superscript 1]p. 269
Three-manifold invariant
Improved partition functionp. 272
Values of the invariantp. 278
Abelian surgery invariant
Compact Abelian theoryp. 283
Abelian surgery rulesp. 289
Abelian surgery invariantp. 292
Referencesp. 303
Subject Indexp. 311
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783110140286
ISBN-10: 3110140284
Series: De Gruyter Expositions in Mathematics
Audience: Professional
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 326
Published: 1st August 1993
Publisher: De Gruyter
Country of Publication: DE
Dimensions (cm): 23.0 x 15.5  x 2.54
Weight (kg): 0.7