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La Q-dérive d'ordre N modes collectifs moléculaire en nucléaire Q-déformes / Raouf Beddiaf
Titre : La Q-dérive d'ordre N modes collectifs moléculaire en nucléaire Q-déformes Type de document : texte imprimé Auteurs : Raouf Beddiaf ; A. Bouldjedri, Directeur de thèse Editeur : Setif:UFA Année de publication : 2000 Importance : 1 vol (76 f .) Format : 29 cm Catégories : Thèses & Mémoires:Physique Mots-clés : Groupe quantique
Q-dérive d'ordre n
Q-modes collectifs:molécule C2H4
modèle VMIIndex. décimale : 530 Physique Résumé :
Le présent travail se compose de deux parties dans lesquels on traite une nouvelle classe de symétrie plus étendue de celle de l'algèbre de Lie et qui est l'algèbre quantique (groupe quantique), elle a été introduite pour la première fois en l985 et a pris tes vite de l'importance pour ses diverses applications d ra physique.
La première partie est consacrée d une étude mathématique formelle ou on donne la formulation compacte de l'expression de la q-dérive d'ordre n ainsi que sa vérification pour des fonctions élémentaires (eq(ax), cosu(x),sinq(x)).
Dans la deuxième partie, on étudie les applications de cette algèbre à des systèmes physiques (moléculaire et nucléaire)
La première application est l’étude des q-modes collectifs (rotation + oscillation de torsion) de la molécule C2H4, ou il est important de souligner le fait que cette étude est réalisable par le biais de la formulation bosonique.
La seconde application est l'extension du modèle vlv1l standard par l,introduction d'un troisième paramètre (relie i la q-déformation). Le but de cette extension était de raffiner les valeurs théoriques et avoir un accord avec les donnés expérimentalesCôte titre : MPH/0257,MPH/0202- 0207,MPH/0254 La Q-dérive d'ordre N modes collectifs moléculaire en nucléaire Q-déformes [texte imprimé] / Raouf Beddiaf ; A. Bouldjedri, Directeur de thèse . - [S.l.] : Setif:UFA, 2000 . - 1 vol (76 f .) ; 29 cm.
Catégories : Thèses & Mémoires:Physique Mots-clés : Groupe quantique
Q-dérive d'ordre n
Q-modes collectifs:molécule C2H4
modèle VMIIndex. décimale : 530 Physique Résumé :
Le présent travail se compose de deux parties dans lesquels on traite une nouvelle classe de symétrie plus étendue de celle de l'algèbre de Lie et qui est l'algèbre quantique (groupe quantique), elle a été introduite pour la première fois en l985 et a pris tes vite de l'importance pour ses diverses applications d ra physique.
La première partie est consacrée d une étude mathématique formelle ou on donne la formulation compacte de l'expression de la q-dérive d'ordre n ainsi que sa vérification pour des fonctions élémentaires (eq(ax), cosu(x),sinq(x)).
Dans la deuxième partie, on étudie les applications de cette algèbre à des systèmes physiques (moléculaire et nucléaire)
La première application est l’étude des q-modes collectifs (rotation + oscillation de torsion) de la molécule C2H4, ou il est important de souligner le fait que cette étude est réalisable par le biais de la formulation bosonique.
La seconde application est l'extension du modèle vlv1l standard par l,introduction d'un troisième paramètre (relie i la q-déformation). Le but de cette extension était de raffiner les valeurs théoriques et avoir un accord avec les donnés expérimentalesCôte titre : MPH/0257,MPH/0202- 0207,MPH/0254 Exemplaires (8)
Code-barres Cote Support Localisation Section Disponibilité MPH/0202 MPH/0202- 0207 Mémoire Bibliothéque des sciences Français Disponible
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DisponibleMPH/0203 MPH/0202- 0207 Mémoire Bibliothéque des sciences Français Disponible
DisponibleMPH/0205 MPH/0202- 0207 Mémoire Bibliothéque des sciences Français Disponible
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DisponibleQualitative aspects and applications of nonlinear evolution equations:Proceedings of the workshop / H.Beirao Da Viega
Titre : Qualitative aspects and applications of nonlinear evolution equations:Proceedings of the workshop Type de document : texte imprimé Auteurs : H.Beirao Da Viega ; Tatsien Li Editeur : Singapore : World scientific Année de publication : 1994 Importance : 1 vol 215 p.) Format : 24 cm ISBN/ISSN/EAN : 978-981-02-1708-2 Catégories : Physique Mots-clés : Physique, Équations nonlinear
Équations à évolution non linéaireIndex. décimale : 530 Physique Note de contenu :
SOMMAIRE
Preface
Part 1 Invited Lectures
Heat Flow Method
A Class of Integrable Systems and Solitons in Higher Dimensional Space-Time Rn+1
Qualitative Behavior of Global Solutions to Inhomogeneous Quasilinear Hyperbolic Systems
On the Geometry of sinh-Gordon Equation
Weak Linear Degeneracy and Lifespan of Classical Solutions for First Order Quasilinear Hyperbolic Systems
Microlocal Order of Singularities for Distributions and Trace Formulas of Hyperbolic Type
Existence and Regularity of Solutions to Nonlinear Thermoelastic Systems
Mixed Problems for Linear Symmetric Hyperbolic Systems with Characteristic Boundary Conditions
The Initial Boundary Value Problem for Symmetric Hyperbolic Systems with Characteristic Boundary
Global Dynamics and Control of a Comprehensive Nonlinear Beam Equation
Part 2 Talks Given at the Seminars
Incompressible Limit of Compressible Navier-Stokes Equations
Sobolev Inequalities Associated with Conormal Vector Fields
The Differential Equation for the Interface in a Porous Media-Type Equation
Classical Solutions to Singular Hyperbolic Systems Modelling Acoustic Wave Propagation
The Finite Dimensional Behavior of the Global Attractors for the Generalized Landau-Lifshitz Equation on Compact Manifolds
Remarks on the Global Existence in the Dynamics of a Viscous, Heat-Conducting, One-Dimensional Gas
Asymptotic Behavior of a Nonlinear Model for the Geographic Diffusion of Infections Diseases
The Solutions and Algebraic Properties of Two Breaking Soliton Equations
Superstructures in Nonlinear Reaction-Diffusion Equations
Auto-BTs and Multisoliton Solutions of MKdV System
Nonlinear Evolution Equations for Waves in Random Media
The Cauchy Problem for a Class of 2×2 Nonstrictly Hyperbolic System of Conservation Laws
Uniqueness of Global Quasi-Classical Solutions of the Cauchy Problems for First-Order Nonlinear Partial Differential Equations
List of ContributionsCôte titre : Fs/0338 Qualitative aspects and applications of nonlinear evolution equations:Proceedings of the workshop [texte imprimé] / H.Beirao Da Viega ; Tatsien Li . - Singapore : World scientific, 1994 . - 1 vol 215 p.) ; 24 cm.
ISBN : 978-981-02-1708-2
Catégories : Physique Mots-clés : Physique, Équations nonlinear
Équations à évolution non linéaireIndex. décimale : 530 Physique Note de contenu :
SOMMAIRE
Preface
Part 1 Invited Lectures
Heat Flow Method
A Class of Integrable Systems and Solitons in Higher Dimensional Space-Time Rn+1
Qualitative Behavior of Global Solutions to Inhomogeneous Quasilinear Hyperbolic Systems
On the Geometry of sinh-Gordon Equation
Weak Linear Degeneracy and Lifespan of Classical Solutions for First Order Quasilinear Hyperbolic Systems
Microlocal Order of Singularities for Distributions and Trace Formulas of Hyperbolic Type
Existence and Regularity of Solutions to Nonlinear Thermoelastic Systems
Mixed Problems for Linear Symmetric Hyperbolic Systems with Characteristic Boundary Conditions
The Initial Boundary Value Problem for Symmetric Hyperbolic Systems with Characteristic Boundary
Global Dynamics and Control of a Comprehensive Nonlinear Beam Equation
Part 2 Talks Given at the Seminars
Incompressible Limit of Compressible Navier-Stokes Equations
Sobolev Inequalities Associated with Conormal Vector Fields
The Differential Equation for the Interface in a Porous Media-Type Equation
Classical Solutions to Singular Hyperbolic Systems Modelling Acoustic Wave Propagation
The Finite Dimensional Behavior of the Global Attractors for the Generalized Landau-Lifshitz Equation on Compact Manifolds
Remarks on the Global Existence in the Dynamics of a Viscous, Heat-Conducting, One-Dimensional Gas
Asymptotic Behavior of a Nonlinear Model for the Geographic Diffusion of Infections Diseases
The Solutions and Algebraic Properties of Two Breaking Soliton Equations
Superstructures in Nonlinear Reaction-Diffusion Equations
Auto-BTs and Multisoliton Solutions of MKdV System
Nonlinear Evolution Equations for Waves in Random Media
The Cauchy Problem for a Class of 2×2 Nonstrictly Hyperbolic System of Conservation Laws
Uniqueness of Global Quasi-Classical Solutions of the Cauchy Problems for First-Order Nonlinear Partial Differential Equations
List of ContributionsCôte titre : Fs/0338 Exemplaires (1)
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DisponibleQuantitative texture analysis / H-J Bunge
Exemplaires (1)
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DisponibleQuantum field theory and critical phenomena / Zinn-Justin, Jean
Titre : Quantum field theory and critical phenomena Type de document : texte imprimé Auteurs : Zinn-Justin, Jean Editeur : Oxford University Press Année de publication : 2002 Importance : 1 vol. (1054 p.) Format : 24 cm ISBN/ISSN/EAN : 978-0-19-850923-3 Note générale : 978-0-19-850923-3 Langues : Anglais (eng) Catégories : Physique Mots-clés : physique Index. décimale : 530 Physique Résumé :
The book is an introduction to quantum field theory and renormalization group.It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This advanced new edition is based on graduate courses and summer schools given by the author over a number of years. Although there are several good textbooks on QFT, this is the first to emphasize the common aspects of particle physics and the theory of critical phenomena in a unified framework. The book has been fully updated, with about 50% new material added. Three new chapters have been included: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chaper on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory. Exercises that were originally included in previous editions will be supplied online at www-spht.ceafr/articles/T02/001.Côte titre : Fs/14184-14186 Quantum field theory and critical phenomena [texte imprimé] / Zinn-Justin, Jean . - [S.l.] : Oxford University Press, 2002 . - 1 vol. (1054 p.) ; 24 cm.
ISBN : 978-0-19-850923-3
978-0-19-850923-3
Langues : Anglais (eng)
Catégories : Physique Mots-clés : physique Index. décimale : 530 Physique Résumé :
The book is an introduction to quantum field theory and renormalization group.It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This advanced new edition is based on graduate courses and summer schools given by the author over a number of years. Although there are several good textbooks on QFT, this is the first to emphasize the common aspects of particle physics and the theory of critical phenomena in a unified framework. The book has been fully updated, with about 50% new material added. Three new chapters have been included: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chaper on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory. Exercises that were originally included in previous editions will be supplied online at www-spht.ceafr/articles/T02/001.Côte titre : Fs/14184-14186 Exemplaires (3)
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DisponibleFs/14186 Fs/14184-14186 livre Bibliothéque des sciences Anglais Disponible
DisponibleQuantum groups in two-dimensional physics / Gómez, César
Titre : Quantum groups in two-dimensional physics Type de document : texte imprimé Auteurs : Gómez, César Editeur : Cambridge : Cambridge university press Année de publication : 1996 Importance : 1 vol. (457 p.) Format : 29 cm ISBN/ISSN/EAN : 978-0-521-46065-1 Note générale : 978-0-521-46065-1 Langues : Anglais (eng) Catégories : Physique Mots-clés : physique Index. décimale : 530 Physique Résumé :
The book is an introduction to quantum field theory and renormalization group.It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This advanced new edition is based on graduate courses and summer schools given by the author over a number of years. Although there are several good textbooks on QFT, this is the first to emphasize the common aspects of particle physics and the theory of critical phenomena in a unified framework. The book has been fully updated, with about 50% new material added. Three new chapters have been included: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chaper on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory. Exercises that were originally included in previous editions will be supplied online at www-spht.ceafr/articles/T02/001.Note de contenu :
Sommaire
Preface xv
1 5-matrices, spin chains and vertex models 1
1.1 Factorized S -matrix models 1
1.1.1 Zamolodchikov algebra 5
1.1.2 Example 7
1.2 Bethe's diagonalization of spin chain hamiltonians 10
1.3 Integrable vertex models: the six-vertex model 14
Exercises 25
Appendix A Form factors 28
A 1.1 Introduction to Smirnov's program 28
A1.2 Form factors at work: the Ising model 31
Exercise 33
2 The Yang-Baxter equation: a first look 34
2.1 The Yang-Baxter algebra 34
2.1.1 The ^-matrix and the Yang-Baxter equation 34
2.1.2 The monodromy matrix 38
2.1.3 Co-product and the Yang-Baxter algebra 39
2.1.4 Algebraic Bethe ansatz 41
2.2 Yang-Baxter algebras and braid groups 47
2.3 Yang-Baxter algebras and quantum groups 51
2.3.1 The ^-matrix as an intertwiner 53
2.3.2 A first contact with affine Hopf algebras 55
2.4 Descendants of the six-vertex model 58
2.4.1 Descent procedure 58
2.4.2 Bethe ansatz for descendant models 61
2.5 Comments 66
2.5.1 Explanation of our conventions 66
2.5.2 On parametrizations of the six-vertex weights 67
Exercises 67
3 Bethe ansatz: some examples 71
3.1 Introduction and summary 71
3.2 The phase structure of the six-vertex model 73
ix
Cambridge University Press
978-0-521-46065-1 - Quantum Groups in Two-Dimensional Physics
César Gómez, Martà Ruiz-Altaba and Germán Sierra
Frontmatter
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© in this web service Cambridge University Press www.cambridge.org
x Contents
3.3 Low lying excitations 78
3.3.1 Strings and holes 78
3.3.2 Dispersion relations 83
3.4 Integrable higher-spin chains 83
3.4.1 Hidden symmetry 85
3.5 Integrability in a box: open boundary conditions 88
3.5.1 Vertex models: the Sklyanin equation 88
3.5.2 Spin chains: the Bethe ansatz 92
3.6 Hamiltonians with quantum group invariance 96
3.7 Spin-1 chains 98
Exercises 102
4 The eight-vertex model 108
4.1 Definitions and Yang-Baxter relations 108
4.2 Bethe ansatz solution 111
4.2.1 A smart change of basis 112
4.2.2 Eight-vertex Yang-Baxter algebra 116
4.3 Reference state and 8 parameter 118
4.3.1 Further comments on the 0 parameter 120
Exercises 121
Appendix B Elliptic functions 125
Exercises 128
Appendix C Sklyanin algebra 130
Exercises 132
5 Face models 134
5.1 Weights and graphs: the definitions 134
5.2 Trigonometric solutions 137
5.2.1 Bratelli diagrams 137
5.2.2 Yang-Baxter operators 138
5.2.3 The Temperley-Lieb-Jones algebra 139
5.2.4 Towers of algebras associated with a graph 140
5.2.5 The algebra of face observables 144
5.2.6 The trigonometric solution for Coxeter models 146
5.3 Elliptic solutions 148
5.3.1 An example: the Ising model 148
5.3.2 Restricted and unrestricted models 154
5.4 Fusion for face models 155
5.5 The corner transfer matrix 158
Exercises 160
Appendix D Knots and integrable models 165
D5.1 Introduction: the Jones polynomial 165
D5.2 Markov moves 168
D5.3 Markov traces for the Hecke algebra 170
Cambridge University Press
978-0-521-46065-1 - Quantum Groups in Two-Dimensional Physics
César Gómez, Martà Ruiz-Altaba and Germán Sierra
Frontmatter
More information
© in this web service Cambridge University Press www.cambridge.org
Contents xi
D5.4 The Burau representation 172
D5.5 Extended Yang-Baxter systems 173
Exercises 176
Appendix E Spin models 177
E5.1 Factors and subfactors 177
E5.2 Spin models 180
Exercises 183
6 Quantum groups: mathematical review 184
6.1 Hopf algebras 184
6.2 Quasi-triangular Hopf algebras 186
6.3 Drinfeld's quantum double 187
6.4 The quantum group Uq(st(2)) 189
6.4.1 Quantum double construction 189
6.4.2 Irreducible representations 194
6.5 Centralizer and Hecke algebra 201
6.5.1 Representations of Hn(q) 203
6.6 Link invariants from quantum groups 205
6.7 The quantum group Uq(9) 207
6.8 ^-matrices: an incomplete catalog 208
6.9 Classical Yang-Baxter equation 210
6.10 Affine quantum groups 211
6.11 Quasi-Hopf algebras 218
Exercises 219
7 Integrable models at roots of unity 228
7.1 Mathematical preliminaries 228
7.1.1 The center of Uq(sf(2)) 228
7.1.2 Finite-dimensional irreps 229
7.1.3 The co-adjoint action 231
7.1.4 Intertwiners 234
7.2 A family of ^-matrices 235
7.2.1 Highest weight intertwiner 235
7.2.2 The nilpotent K-matrix 238
7.3 Nilpotent hamiltonians 240
7.4 Bethe ansatz 244
7.5 The limit £ -> oo 250
7.5.1 Quantum harmonic oscillators 251
7.5.2 Link invariants 252
7.6 The chiral Potts model 252
7.6.1 Star-triangle relations 255
7.6.2 The associated spin chain hamiltonian 258
7.6.3 Self-dual chiral Potts models 260
7.6.4 Super-integrable chiral Potts models 262
Cambridge University Press
978-0-521-46065-1 - Quantum Groups in Two-Dimensional Physics
César Gómez, Martà Ruiz-Altaba and Germán Sierra
Frontmatter
More information
© in this web service Cambridge University Press www.cambridge.org
xii Contents
7.6.5 The quantum symmetry 263
7.7 Solving the Yang-Baxter equation 268
Exercises 269
8 Two-dimensional conformal field theories 272
8.1 Introduction: critical phenomena 272
8.2 Renormalization group 272
8.3 Examples 275
8.3.1 The one-dimensional Ising model 275
8.3.2 The gaussian model 278
8.4 Operator algebra of a universality class 280
8.5 Conformal invariance and statistical mechanics 281
8.6 The two-dimensional conformal group 282
8.7 Representations of the Virasoro algebra 286
8.8 Decoupling of null vectors 291
8.8.1 The Kac formula 292
8.8.2 Conformal Ward identities 294
8.8.3 Minimal models 295
8.9 Fusion algebra 299
8.10 Finite-size effects 300
Exercises 304
9 Duality in conformal field theories 308
9.1 Monodromy invariance 309
9.2 Conformal blocks and chiral vertex operators 311
9.3 Sewing 314
9.4 Braiding and fusion 319
9.5 Conformal field theories and towers of algebras 323
9.6 Genus one polynomial equations 327
Exercises 336
10 Coulomb gas representation 340
10.1 Free and Feigin-Fuks scalar fields 340
10.2 Screening charges in correlation functions 344
10.2.1 Braiding matrices: an explicit example 348
10.2.2 Contour techniques 350
10.3 Lagrangian approach 353
10.4 Wess-Zumino models 355
10.4.1 The Knizhnik-Zamolodchikov equation 355
10.4.2 Free field representation of Wess-Zumino models 359
10.4.3 The Goddard-Kent-Olive construction 363
10.5 Magic corner transfer matrix 365
Exercises 366
Appendix F Vertex operators
11 Quantum groups in conformal field theory 376
11.1 The hidden quantum symmetry 376
11.2 Braiding matrices and quantum 6j symbols 381
11.3 Ribbon Hopf algebras 384
11.4 The contour representation of quantum groups 386
11.4.1 Screened vertex operators 386
11.4.2 Examples 390
11.4.3 The quantum qroup 392
11.4.4 The ^-matrix 396
11.4.5 Chiral vertex operators 400
11.5 The quantum group of SU(2)k 401
11.5.1 The ^-matrix 407
11.5.2 Fusion rules and chiral vertex operators 409
11.5.3 On intertwiners: a clarification 413
11.6 The quantum group of minimal models 413
Exercises 415
Appendix G Super-conformal field theories 422
Gll.l Super-conformal transformations 422
G11.2 Representations 424
G11.3 N = 2 super-conformal algebras 425
G11.4 N = 2 irreps and the chiral ring 426
G11.5 N = 2 topological theories 429
G11.6 Perturbed chiral ring 430
G11.7 Landau-Ginsburg description 432
G11.8 Quantum groups and solitons 434
Exercise 437
ReferencesCôte titre : Fs/14187-14188 Quantum groups in two-dimensional physics [texte imprimé] / Gómez, César . - Cambridge : Cambridge university press, 1996 . - 1 vol. (457 p.) ; 29 cm.
ISBN : 978-0-521-46065-1
978-0-521-46065-1
Langues : Anglais (eng)
Catégories : Physique Mots-clés : physique Index. décimale : 530 Physique Résumé :
The book is an introduction to quantum field theory and renormalization group.It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This advanced new edition is based on graduate courses and summer schools given by the author over a number of years. Although there are several good textbooks on QFT, this is the first to emphasize the common aspects of particle physics and the theory of critical phenomena in a unified framework. The book has been fully updated, with about 50% new material added. Three new chapters have been included: an introduction to non-relativistic quantum statistical physics; a chapter on critical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chaper on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted to critical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory. Exercises that were originally included in previous editions will be supplied online at www-spht.ceafr/articles/T02/001.Note de contenu :
Sommaire
Preface xv
1 5-matrices, spin chains and vertex models 1
1.1 Factorized S -matrix models 1
1.1.1 Zamolodchikov algebra 5
1.1.2 Example 7
1.2 Bethe's diagonalization of spin chain hamiltonians 10
1.3 Integrable vertex models: the six-vertex model 14
Exercises 25
Appendix A Form factors 28
A 1.1 Introduction to Smirnov's program 28
A1.2 Form factors at work: the Ising model 31
Exercise 33
2 The Yang-Baxter equation: a first look 34
2.1 The Yang-Baxter algebra 34
2.1.1 The ^-matrix and the Yang-Baxter equation 34
2.1.2 The monodromy matrix 38
2.1.3 Co-product and the Yang-Baxter algebra 39
2.1.4 Algebraic Bethe ansatz 41
2.2 Yang-Baxter algebras and braid groups 47
2.3 Yang-Baxter algebras and quantum groups 51
2.3.1 The ^-matrix as an intertwiner 53
2.3.2 A first contact with affine Hopf algebras 55
2.4 Descendants of the six-vertex model 58
2.4.1 Descent procedure 58
2.4.2 Bethe ansatz for descendant models 61
2.5 Comments 66
2.5.1 Explanation of our conventions 66
2.5.2 On parametrizations of the six-vertex weights 67
Exercises 67
3 Bethe ansatz: some examples 71
3.1 Introduction and summary 71
3.2 The phase structure of the six-vertex model 73
ix
Cambridge University Press
978-0-521-46065-1 - Quantum Groups in Two-Dimensional Physics
César Gómez, Martà Ruiz-Altaba and Germán Sierra
Frontmatter
More information
© in this web service Cambridge University Press www.cambridge.org
x Contents
3.3 Low lying excitations 78
3.3.1 Strings and holes 78
3.3.2 Dispersion relations 83
3.4 Integrable higher-spin chains 83
3.4.1 Hidden symmetry 85
3.5 Integrability in a box: open boundary conditions 88
3.5.1 Vertex models: the Sklyanin equation 88
3.5.2 Spin chains: the Bethe ansatz 92
3.6 Hamiltonians with quantum group invariance 96
3.7 Spin-1 chains 98
Exercises 102
4 The eight-vertex model 108
4.1 Definitions and Yang-Baxter relations 108
4.2 Bethe ansatz solution 111
4.2.1 A smart change of basis 112
4.2.2 Eight-vertex Yang-Baxter algebra 116
4.3 Reference state and 8 parameter 118
4.3.1 Further comments on the 0 parameter 120
Exercises 121
Appendix B Elliptic functions 125
Exercises 128
Appendix C Sklyanin algebra 130
Exercises 132
5 Face models 134
5.1 Weights and graphs: the definitions 134
5.2 Trigonometric solutions 137
5.2.1 Bratelli diagrams 137
5.2.2 Yang-Baxter operators 138
5.2.3 The Temperley-Lieb-Jones algebra 139
5.2.4 Towers of algebras associated with a graph 140
5.2.5 The algebra of face observables 144
5.2.6 The trigonometric solution for Coxeter models 146
5.3 Elliptic solutions 148
5.3.1 An example: the Ising model 148
5.3.2 Restricted and unrestricted models 154
5.4 Fusion for face models 155
5.5 The corner transfer matrix 158
Exercises 160
Appendix D Knots and integrable models 165
D5.1 Introduction: the Jones polynomial 165
D5.2 Markov moves 168
D5.3 Markov traces for the Hecke algebra 170
Cambridge University Press
978-0-521-46065-1 - Quantum Groups in Two-Dimensional Physics
César Gómez, Martà Ruiz-Altaba and Germán Sierra
Frontmatter
More information
© in this web service Cambridge University Press www.cambridge.org
Contents xi
D5.4 The Burau representation 172
D5.5 Extended Yang-Baxter systems 173
Exercises 176
Appendix E Spin models 177
E5.1 Factors and subfactors 177
E5.2 Spin models 180
Exercises 183
6 Quantum groups: mathematical review 184
6.1 Hopf algebras 184
6.2 Quasi-triangular Hopf algebras 186
6.3 Drinfeld's quantum double 187
6.4 The quantum group Uq(st(2)) 189
6.4.1 Quantum double construction 189
6.4.2 Irreducible representations 194
6.5 Centralizer and Hecke algebra 201
6.5.1 Representations of Hn(q) 203
6.6 Link invariants from quantum groups 205
6.7 The quantum group Uq(9) 207
6.8 ^-matrices: an incomplete catalog 208
6.9 Classical Yang-Baxter equation 210
6.10 Affine quantum groups 211
6.11 Quasi-Hopf algebras 218
Exercises 219
7 Integrable models at roots of unity 228
7.1 Mathematical preliminaries 228
7.1.1 The center of Uq(sf(2)) 228
7.1.2 Finite-dimensional irreps 229
7.1.3 The co-adjoint action 231
7.1.4 Intertwiners 234
7.2 A family of ^-matrices 235
7.2.1 Highest weight intertwiner 235
7.2.2 The nilpotent K-matrix 238
7.3 Nilpotent hamiltonians 240
7.4 Bethe ansatz 244
7.5 The limit £ -> oo 250
7.5.1 Quantum harmonic oscillators 251
7.5.2 Link invariants 252
7.6 The chiral Potts model 252
7.6.1 Star-triangle relations 255
7.6.2 The associated spin chain hamiltonian 258
7.6.3 Self-dual chiral Potts models 260
7.6.4 Super-integrable chiral Potts models 262
Cambridge University Press
978-0-521-46065-1 - Quantum Groups in Two-Dimensional Physics
César Gómez, Martà Ruiz-Altaba and Germán Sierra
Frontmatter
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xii Contents
7.6.5 The quantum symmetry 263
7.7 Solving the Yang-Baxter equation 268
Exercises 269
8 Two-dimensional conformal field theories 272
8.1 Introduction: critical phenomena 272
8.2 Renormalization group 272
8.3 Examples 275
8.3.1 The one-dimensional Ising model 275
8.3.2 The gaussian model 278
8.4 Operator algebra of a universality class 280
8.5 Conformal invariance and statistical mechanics 281
8.6 The two-dimensional conformal group 282
8.7 Representations of the Virasoro algebra 286
8.8 Decoupling of null vectors 291
8.8.1 The Kac formula 292
8.8.2 Conformal Ward identities 294
8.8.3 Minimal models 295
8.9 Fusion algebra 299
8.10 Finite-size effects 300
Exercises 304
9 Duality in conformal field theories 308
9.1 Monodromy invariance 309
9.2 Conformal blocks and chiral vertex operators 311
9.3 Sewing 314
9.4 Braiding and fusion 319
9.5 Conformal field theories and towers of algebras 323
9.6 Genus one polynomial equations 327
Exercises 336
10 Coulomb gas representation 340
10.1 Free and Feigin-Fuks scalar fields 340
10.2 Screening charges in correlation functions 344
10.2.1 Braiding matrices: an explicit example 348
10.2.2 Contour techniques 350
10.3 Lagrangian approach 353
10.4 Wess-Zumino models 355
10.4.1 The Knizhnik-Zamolodchikov equation 355
10.4.2 Free field representation of Wess-Zumino models 359
10.4.3 The Goddard-Kent-Olive construction 363
10.5 Magic corner transfer matrix 365
Exercises 366
Appendix F Vertex operators
11 Quantum groups in conformal field theory 376
11.1 The hidden quantum symmetry 376
11.2 Braiding matrices and quantum 6j symbols 381
11.3 Ribbon Hopf algebras 384
11.4 The contour representation of quantum groups 386
11.4.1 Screened vertex operators 386
11.4.2 Examples 390
11.4.3 The quantum qroup 392
11.4.4 The ^-matrix 396
11.4.5 Chiral vertex operators 400
11.5 The quantum group of SU(2)k 401
11.5.1 The ^-matrix 407
11.5.2 Fusion rules and chiral vertex operators 409
11.5.3 On intertwiners: a clarification 413
11.6 The quantum group of minimal models 413
Exercises 415
Appendix G Super-conformal field theories 422
Gll.l Super-conformal transformations 422
G11.2 Representations 424
G11.3 N = 2 super-conformal algebras 425
G11.4 N = 2 irreps and the chiral ring 426
G11.5 N = 2 topological theories 429
G11.6 Perturbed chiral ring 430
G11.7 Landau-Ginsburg description 432
G11.8 Quantum groups and solitons 434
Exercise 437
ReferencesCôte titre : Fs/14187-14188 Exemplaires (2)
Code-barres Cote Support Localisation Section Disponibilité Fs/14187 Fs/14187-14188 livre Bibliothéque des sciences Anglais Disponible
DisponibleFs/14188 Fs/14187-14188 livre Bibliothéque des sciences Anglais Disponible
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