Dual Superconductor Models of Color Confinement (Lecture Notes in Physics, 639)

✍ Scribed by Georges Ripka

• Publisher: Springer
• Year: 2004
• Tongue: English
• Leaves: 257
• Edition: 2004
• Category: Library

✦ Synopsis

Physicists who wish to understand the modeling of confinement of quantum chromodynamics, as exhibited by dual superconductors, will find this book an excellent introduction. The author focuses on the models themselves, especially the Landau--Ginzburg model of a dual superconductor, also called the Dual Abelian Higgs model. The book addresses graduate students and researchers, and is noteworthy for the remarkable clarity of its exposition.

✦ Table of Contents

front-matter
Chapter 1
Chapter 2
2.1 The Symmetry between Electric and Magnetic Charges at the Level of the Maxwell Equations

2.3 The Current of a Charged Point Particle
2.4 The World Sheet Swept Out a Dirac String in Minkowski Space
2.5 The Euclidean Components of the Dirac String
2.6 Dirac Strings with a Constant Orientation
2.7 The Vector Potential A in the Vicinity of a Magnetic Monopole
2.8 The Irrelevance of the Shape of the Dirac String
2.9 Deformations of Dirac Strings and Charge Quantization
2.10 The Way Dirac Originally Argued for the String

Chapter 3
2.1 The Symmetry between Electric and Magnetic Charges at the Level of the Maxwell Equations

2.3 The Current and World Line of a Charged Particle
2.4 The World Sheet Swept Out by a Dirac String in Minkowski Space
2.6 Dirac Strings with a Constant Orientation
2.7 The Vector Potential A in the Vicinity of a Magnetic Monopole
2.8 The Irrelevance of the Shape of the Dirac String
2.9 Deformations of Dirac Strings and Charge Quantization
2.10 The Way Dirac Originally Argued for the String

Chapter 4
3.1 The Landau-Ginzburg Action of a Dual Superconductor
3.2 The Landau-Ginzburg Action in Terms of Euclidean Fields
3.3 The Energy of Two Equal and Opposite Electric Charges
3.3.1 The Ball-Caticha Expression of the String Term
3.3.2 Deformations of the String and Charge Quantization
3.3.3 The Flux Tube Calculated in the Unitary Gauge
3.3.4 The Electric Field and the Magnetic Current
3.3.5 The Abrikosov-Nielsen-Olesen Vortex
3.3.6 Divergencies of the London Limit
3.4 Comparison of the Landau-Ginzburg Model with Lattice Data
3.5 The Dielectric Function of the Color-Dielectric Model
3.6 The London Limit of the Landau-Ginzburg Model
3.6.1 The Gluon Propagator
3.6.2 The Energy in the Presence of Static Electric Charges in the London Limit
3.6.3 The Con.ning Potential in the London Limit
3.6.4 Chiral Symmetry Breaking
3.7 The Field-Strength Correlator
3.8 The London Limit Expressed in Terms of a Kalb-Ramond Field
3.8.1 The Double Gauge Invariance
3.8.2 The Duality Transformation
3.8.3 The Quanti.cation of the Massive Kalb-Ramond Field
3.8.4 The Elementary Excitations
3.8.5 The Nambu Hierarchy of Gauge Potentials
3.9 The Hamiltonian of the Landau-Ginzburg Model
3.10 The Elementary Excitations of the Landau-Ginzburg Model
3.11 The Two-Potential Zwanziger Formalism

3.11.2 The Zwanziger Action Applied to a Dual Superconductor
3.11.3 Elimination of the Gauge Potential Aµ
Chapter 5
3.1 The Landau-Ginzburg Action of a Dual Superconductor
3.2 The Landau-Ginzburg Action in Terms of Euclidean Fields
3.3 The Flux Tube Joining Two Equal and Opposite Electric Charges
3.3.1 The Ball-Caticha Expression of the String Term
3.3.2 Deformations of the String and Charge Quantization
3.3.3 The Relation Between the Dirac String and the Flux Tube in the Unitary Gauge
3.3.4 The Flux Tube Calculated in the Unitary Gauge
3.3.5 The Electric Field and the Magnetic Current
3.3.6 The Abrikosov-Nielsen-Olesen Vortex
3.3.7 Divergencies of the London Limit
3.4 Comparison of the Landau-Ginzburg Model with Lattice Data
3.5 The Dielectric Function of the Color-Dielectric Model
3.6 The London Limit of the Landau-Ginzburg Model
3.6.1 The Gluon Propagator
3.6.2 The Energy in the Presence of Static Electric Charges in the London Limit
3.6.3 The Con.ning Potential in the London Limit
3.6.4 Chiral Symmetry Breaking
3.7 The Field-Strength Correlator
3.8 The London Limit Expressed in Terms of a Kalb-Ramond Field
3.8.1 The Double Gauge Invariance
3.8.2 The Duality Transformation
3.8.3 The Quanti.cation of the Massive Kalb-Ramond Field
3.8.4 The Elementary Excitations
3.8.5 The Nambu Hierarchy of Gauge Potentials
3.9 The Hamiltonian of the Landau-Ginzburg Model
3.10 The Elementary Excitations of the Landau-Ginzburg Model
3.11 The Two-Potential Zwanziger Formalism

3.11.2 The Zwanziger Action Applied to a Dual Superconductor
3.11.3 Elimination of the Gauge Potential Aµ
Chapter 6
4.1 The Occurrence of Monopoles in an Abelian Gauge
4.1.1 The Magnetic Charge of a SU (2) Monopole
4.1.2 The Magnetic Charges of SU (3) Monopoles
4.2 The Maximal Abelian Gauge
Chapter 7
4.1 The Occurrence of Monopoles in an Abelian Gauge
4.1.1 The Magnetic Charge of a SU (2) Monopole
4.1.2 The Magnetic Charges of SU (3) Monopoles
4.2 The Maximal Abelian Gauge and Abelian Projection
4.3 Abelian and Center Projection on the Lattice
Chapter 8
5.1 An Abelian SU (3) Landau-Ginzburg Model
5.1.1 The Model Action and Its Abelian Gauge Invariance
5.2 The Coupling of Quarks to the Gluon Field
5.3 The Energy of Three Static (Quark) Charges
5.4 Quantization of the Electric and Magnetic Charges
5.5 Flux Tubes Formed by the Electric and Magnetic Fields
5.6 A Weyl Symmetric Form of the Action
Chapter 9
5.1 An Abelian SU (3) Landau-Ginzburg Model
5.1.1 The Model Action and Its Abelian Gauge Invariance
5.2 The Coupling of Quarks to the Gluon Field
5.3 The Energy of Three Static (Quark) Charges
5.4 Quantization of the Electric and Magnetic Charges
5.5 Flux Tubes Formed by the Electric and Magnetic Fields
5.6 A Weyl Symmetric Form of the Action
Chapter 10
A.1 Compact Notation
A.
A.3 Vectors and Their Dual Form
A.3.1 Longitudinal and Transverse Components of Vectors
A.3.2 Identities Involving Vectors
A.3.3 Identities Involving Vectors and Antisymmetric Tensors
A.4 Antisymmetric Tensors and Their Dual Form
A.4.1 The Dual of an Antisymmetric Tensor
A.4.2 The Zwanziger Identities
A.4.3 Longitudinal and Transverse Components of Antisymmetric Tensors
A.5 Antisymmetric and Dual 3-Forms
A.6 Three-Dimensional Euclidean Vectors
A.6.1 Cartesian Coordinates
A.6.2 Cylindrical Coordinates
A.6.3 Spherical Coordinates
Chapter 11
A.1 Compact Notation
A.
A.3 Vectors and Their Dual Form
A.3.1 Longitudinal and Transverse Components of Vectors
A.3.2 Identities Involving Vectors
A.3.3 Identities Involving Vectors and Antisymmetric Tensors
A.4 Antisymmetric Tensors and Their Dual Form
A.4.1 The Dual of an Antisymmetric Tensor
A.4.2 The Zwanziger Identities
A.4.3 Longitudinal and Transverse Components of Antisymmetric Tensors
A.5 Antisymmetric and Dual 3-Forms
A.6 Three-Dimensional Euclidean Vectors
A.6.1 Cartesian Coordinates
A.6.2 Cylindrical Coordinates
A.6.3 Spherical Coordinates
Chapter 12
Chapter 13
Chapter 14
C.1 The SU (2) Generators
C.2 The SU (3) Generators and Root Vectors
C.3 Root Vectors of SU (3)
Chapter 15
D.1 SU (2) Color Charges
D.2 SU (3) Color Charges
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