Francoise J.-P., Naber G.L., Tsun T.S. (editors) Encyclopedia of Mathematical Physics
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Symmetries in Quantum Field Theory: Algebraic
Aspects 5:179
Symmetries in Quantum Field Theory of Lower
Spacetime Dimensions 5:172
Symmetry Breaking in Field Theory 5:198
Two-Dimensional Models 5:328
Thermal Quantum Field Theory 5:227
Tomita–Takesaki Modular Theory 5:251
Topological Defects and Their Homotopy
Classification 5:257
Twistor Theory: Some Applications 5:303
Quantum Gravity
Knot Invariants and Quantum Gravity 3:215
Knot Theory and Physics 3:220
Loop Quantum Gravity 3:339
Quantum Cosmology 4:153
Quantum Dynamics in Loop Quantum
Gravity 4:165
Quantum Field Theory in Curved
Spacetime 4:202
Quantum Geometry and Its Applications 4:230
Spin Foams 4:645
Wheeler–De Witt Theory 5:453
Quantum Information and Computation
Capacities Enhanced By Entanglement 1:418
Capacity for Quantum Information 1:424
Channels in Quantum Information Theory 1:472
Entanglement 2:228
Entanglement Measures 2:233
Finite Weyl Systems 2:328
Optimal Cloning of Quantum States 3:628
Quantum Channels: Classical Capacity 4:142
Quantum Entropy 4:177
Quantum Error Correction and Fault
Tolerance 4:196
Source Coding in Quantum Information
Theory 4:609
Quantum Mechanics
Aharonov–Bohm Effect 1:191
Arithmetic Quantum Chaos 1:212
Coherent States 1:537
Geometric Phases 2:528
h-Pseudodifferential Operators and
Applications 2:701
N-particle Quantum Scattering 3:585
Normal Forms and Semiclassical
Approximation 3:578
Quantum Entropy 4:177
Quantum Ergodicity and Mixing of
Eigenfunctions 4:183
Quantum Mechanical Scattering
Theory 4:251
Quantum Mechanics: Foundations 4:260
Quantum Mechanics: Generalizations 4:265
Quantum Mechanics: Weak Measurements 4:276
Quantum n-Body Problem 4:283
Quantum Spin Systems 4:295
Quasiperiodic Systems 4:308
Schro¨ dinger Operators 4:487
Stability of Matter 5:8
Stationary Phase Approximation 5:44
Supersymmetric Quantum Mechanics 5:145
Topological Defects and Their Homotopy
Classification 5:257
String Theory and M-Theory
AdS/CFT Correspondence 1:174
Brane Construction of Gauge Theories 1:360
Branes and Black Hole Statistical
Mechanics 1:373
Brane Worlds 1:367
Calibrated Geometry and Special Lagrangian
Submanifolds 1:398
Compactification of Superstring Theory 1:586
Derived Categories 2:41
Fourier–Mukai Transform in String Theory 2:379
Gauge Theories from Strings 2:463
Large-N and Topological Strings 3:263
Large-N Dualities 3:269
Mirror Symmetry: A Geometric Survey 3:439
Noncommutative Geometry from Strings 3:515
Random Algebraic Geometry, Attractors and
Flux Vacua 4:323
Riemannian Holonomy Groups and Exceptional
Holonomy 4:441
String Field Theory 5:94
String Theory: Phenomenology 5:103
String Topology: Homotopy and Geometric
Perspectives 5:111
Superstring Theories 5:133
Twistor Theory: Some Applications 5:303
Two-Dimensional Conformal Field Theory and
Vertex Operator Algebras 5:317
Yang–Mills Theory see Gauge Theory
RELATED MATHEMATICS
SUBJECTS
Algebraic Techniques
Affine Quantum Groups 1:183
Braided and Modular Tensor Categories 1:351
Clifford Algebras and Their
Representations 1:518
Derived Categories 2:41
Finite-Dimensional Algebras and Quivers 2:313
Finite Group Symmetry Breaking 2:322
Hopf Algebras and Q-Deformation Quantum
Groups 2:687
Operads 3:609
CONTENTS LIST BY SUBJECT xxxv
Algebraic Topology
Characteristic Classes 1:488
Cohomology Theories 1:545
Derived Categories 2:41
Equivariant Cohomology and the Cartan
Model 2:242
Fourier–Mukai Transform in String
Theory 2:379
Index Theorems 3:23
Intersection Theory 3:151
K-theory 3:246
Mathai–Quillen Formalism 3:390
Operads 3:609
Spectral Sequences 4:623
String Topology: Homotopy and Geometric
Perspectives 5:111
Complex Geometry
Derived Categories 2:41
Gauge Theory: Mathematical Applications 2:468
Fourier–Mukai Transform in String Theory 2:379
Knot Homologies 3:208
Mirror Symmetry: A Geometric Survey 3:439
Moduli Spaces: An Introduction 3:449
Quillen Determinant 4:315
Riemann Surfaces 4:419
Riemann–Hilbert Problem 4:436
Several Complex Variables: Basic Geometric
Theory 4:540
Several Complex Variables: Compact
Manifolds 4:551
Twistor Theory: Some Applications 5:303
Differential Geometry
Calibrated Geometry and Special Lagrangian
Submanifolds 1:398
Capillary Surfaces 1:431
Characteristic Classes 1:488
Derived Categories 2:41
Einstein Manifolds 2:182
Fourier–Mukai Transform in String Theory 2:379
Gauge Theory: Mathematical Applications 2:468
Index Theorems 3:23
Intersection Theory 3:151
K-Theory 3:246
Lorentzian Geometry 3:343
Mathai-Quillen Formalism 3:390
Moduli Spaces: An Introduction 3:449
Quillen Determinant 4:315
Pseudo-Riemannian Nilpotent Lie Groups 4:94
Riemann-Hilbert Problem 4:436
Riemannian Holonomy Groups and Exceptional
Holonomy 4:441
Singularity and Bifurcation Theory 4:588
Supermanifolds 5:128
Twistor Theory: Some Applications 5:303
Discrete Mathematics
Arithmetic Quantum Chaos 1:212
Combinatorics: Overview 1:553
Number Theory in Physics 3:600
Quasiperiodic Systems 4:308
Functional Analysis and Operator
Algebras
Ba¨cklund Transformations 1:241
C*-Algebras and their Classification 1:393
Coherent States 1:537
Free Probability Theory 2:417
Functional Integration in Quantum Physics 2:434
Gauge Theory: Mathematical Applications 2:468
h-Pseudodifferential Operators and
Applications 2:701
The Jones Polynomial 3:179
K-Theory 3:246
Leray–Schauder Theory and Mapping
Degree 3:281
Ljusternik–Schnirelman Theory 3:328
Ordinary Special Functions 3:637
Positive Maps on C*-Algebras 4:88
Quantum Dynamical Semigroups 4:159
Saddle Point Problems 4:447
Spectral Theory of Linear Operators 4:633
Tomita–Takesaki Modular Theory 5:251
von Neumann Algebras: Introduction, Modular
Theory, and Classification Theory 5:379
von Neumann Algebras: Subfactor Theory 5:385
Wavelets: Applications 5:420
Wavelets: Mathematical Theory 5:426
Lie Groups and Lie Algebras
Classical Groups and Homogeneous Spaces 1:500
Compact Groups and Their
Representations 1:576
Finite-Dimensional Algebras and Quivers 2:313
Lie Groups: General Theory 3:286
Lie Superalgebras and Their
Representations 3:305
Lie, Symplectic, and Poisson Groupoids and Their
Lie Algebroids 3:312
Pseudo-Riemannian Nilpotent Lie Groups 4:94
Riemann–Hilbert Problem 4:436
Solitons and Kac–Moody Lie Algebras 4:594
Low Dimensional Geometry
Finite-type Invariants of 3-Manifolds 2:348
Floer Homology 2:356
Four-manifold Invariants and Physics 2:386
Gauge Theoretic Invariants of 4-Manifolds 2:457
Gauge Theory: Mathematical Applications 2:468
The Jones Polynomial 3:179
Knot Invariants and Quantum Gravity 3:215
Large-N and Topological Strings 3:263
xxxvi CONTENTS LIST BY SUBJECT
Quantum 3-Manifold Invariants 4:117
Singularities of the Ricci Flow 4:584
Twistor Theory: Some Applications 5:303
Noncommutative Geometry
Hopf Algebra Structure of Renormalizable
Quantum Field Theory 2:678
Noncommutative Geometry and the Standard
Model 3:509
Noncommutative Geometry from Strings 3:515
Noncommutative Tori, Yang-Mills, and String
Theory 3:524
Path Integrals in Noncommutative Geometry 4:8
Quantum Group Differentials, Bundles and Gauge
Theory 4:236
Quantum Hall Effect 4:244
Riemann–Hilbert Problem 4:436
Ordinary and Partial Differential
Equations
Bifurcation Theory 1:275
Boltzmann Equation (Classical and
Quantum) 1:306
Boundary Control Method and Inverse Problems
of Wave Propagation 1:340
Capillary Surfaces 1:431
Cauchy Problem for Burgers-Type Equations 1:446
Elliptic Differential Equations: Linear
Theory 2:216
Evolution Equations: Linear and Nonlinear 2:265
Fluid Mechanics: Numerical Methods 2:365
Ginzburg–Landau Equation 2:547
Image Processing: Mathematics 3:1
Inequalities in Sobolev Spaces 3:32
Isomonodromic Deformations 3:173
Kinetic Equations 3:200
Localization For Quasiperiodic Potentials 3:333
Magnetic Resonance Imaging 3:367
Minimal Submanifolds 3:420
Painleve´ Equations 4:1
Partial Differential Equations: Some Examples 4:6
Relativistic Wave Equations Including Higher Spin
Fields 4:391
Riemann–Hilbert Problem 4:436
Semilinear Wave Equations 4:518
Separation of Variables for Differential
Equations 4:526
Stationary Phase Approximation 5:44
Symmetric Hyperbolic Systems and Shock
Waves 5:160
Wave Equations and Diffraction 5:401
Quantization Methods and Path
Integration
Coherent States 1:537
Deformation Quantization 2:1
Deformation Quantization and Representation
Theory 2:9
Deformation Theory 2:16
Deformations of the Poisson Bracket on a
Symplectic Manifold 2:24
Fedosov Quantization 2:291
Feynman Path Integrals 2:307
Functional Integration in Quantum Physics 2:434
Path Integrals in Noncommutative Geometry 4:8
Regularization for Dynamical -Functions 4:386
Quantum Groups
Affine Quantum Groups 1:183
Bicrossproduct Hopf Algebras and
Noncommutative Spacetime 1:265
Braided and Modular Tensor Categories 1:351
Classical r-Matrices, Lie Bialgebras, and Poisson Lie
Groups 1:511
Hopf Algebras and q-Deformation Quantum
Groups 2:687
Hopf Algebra Structure of Renormalizable
Quantum Field Theory 2:678
q-Special Functions 4:105
Quantum Group Differentials, Bundles and Gauge
Theory 4:236
Yang–Baxter Equations 5:465
Stochastic Methods
Determinantal Random Fields 2:47
Free Probability Theory 2:417
Growth Processes in Random Matrix
Theory 2:586
Integrable Systems in Random Matrix
Theory 3:102
Lagrangian Dispersion (Passive Scalar) 3:255
Malliavin Calculus 3:383
Measure on Loop Spaces 3:413
Random Matrix Theory in Physics 4:338
Random Partitions 4:347
Random Walks in Random Environments 4:353
Stochastic Differential Equations 5:63
Stochastic Hydrodynamics 5:71
Stochastic Loewner Evolutions 5:80
Supersymmetry Methods in Random Matrix
Theory 5:151
Symmetry Classes in Random Matrix
Theory 5:204
Symplectic Geometry and Topology
Classical r-Matrices, Lie Bialgebras, and Poisson Lie
Groups 1:511
Contact Manifolds 1:631
Deformations of the Poisson Bracket on a
Symplectic Manifold 2:24
Fedosov Quantization 2:291
Floer Homology 2:356
Graded Poisson Algebras 2:560
CONTENTS LIST BY SUBJECT xxxvii
Hamiltonian Group Actions 2:600
Mirror Symmetry: A Geometric Survey 3:439
Multi-Hamiltonian Systems 3:459
Recursion Operators in Classical
Mechanics 4:371
Singularity and Bifurcation Theory 4:588
Stationary Phase Approximation 5:44
Variational Techniques
Capillary Surfaces 1:431
Control Problems in Mathematical Physics 1:636
Convex Analysis and Duality Methods 1:642
Free Interfaces and Free Discontinuities: Variational
Problems 2:411
-Convergence and Homogenization 2:449
Gauge Theory: Mathematical Applications 2:468
Geometric Measure Theory 2:520
Hamilton–Jacobi Equations and Dynamical
Systems: Variational Aspects 2:636
Minimax Principle in the Calculus of
Variations 3:432
Optimal Transportation 3:632
Variational Techniques for Ginzburg–Landau
Energies 5:355
Variational Techniques for Microstructures 5:363
xxxviii CONTENTS LIST BY SUBJECT
CONTENTS
VOLUME 1
Introductory Article: Classical Mechanics G Gallavotti 1
Introductory Article: Differential Geometry S Paycha 33
Introductory Article: Electromagnetism N M J Woodhouse 40
Introductory Article: Equilibrium Statistical Mechanics G Gallavotti 51
Introductory Article: Functional Analysis S Paycha 88
Introductory Article: Minkowski Spacetime and Special Relativity G L Naber 96
Introductory Article: Quantum Mechanics G F dell’Antonio 109
Introductory Article: Topology Tsou Sheung Tsun 131
A
Abelian and Nonabelian Gauge Theories Using Differential Forms A C Hirshfeld 141
Abelian Higgs Vortices J M Speight 151
Adiabatic Piston Ch Gruber and A Lesne 160
AdS/CFT Correspondence C P Herzog and I R Klebanov 174
Affine Quantum Groups G W Delius and N MacKay 183
Aharonov–Bohm Effect M Socolovsky 191
Algebraic Approach to Quantum Field Theory R Brunetti and K Fredenhagen 198
Anderson Localization see Localization for Quasiperiodic Potentials
Anomalies S L Adler 205
Arithmetic Quantum Chaos J Marklof 212
Asymptotic Structure and Conformal Infinity J Frauendiener 221
Averaging Methods A I Neishtadt 226
Axiomatic Approach to Topological Quantum Field Theory C Blanchet and V Turaev 232
Axiomatic Quantum Field Theory B Kuckert 234
B
Ba
¨
cklund Transformations D Levi 241
Batalin–Vilkovisky Quantization A C Hirshfeld 247
Bethe Ansatz M T Batchelor 253
BF Theories M Blau 257
Bicrossproduct Hopf Algebras and Noncommutative Spacetime S Majid 265
Bifurcation Theory M Haragus and G Iooss 275
Bifurcations in Fluid Dynamics G Schneider 281
Bifurcations of Periodic Orbits J-P Fran¸ oise 285
Bi-Hamiltonian Methods in Soliton Theory M Pedroni 290
Billiards in Bounded Convex Domains S Tabachnikov 296
Black Hole Mechanics A Ashtekar 300
Boltzmann Equation (Classical and Quantum) M Pulvirenti 306
Bose–Einstein Condensates F Dalfovo, L P Pitaevskii and S Stringari 312
Bosons and Fermions in External Fields E Langmann 318
Boundaries for Spacetimes S G Harris 326
Boundary Conformal Field Theory J Cardy 333
Boundary Control Method and Inverse Problems of Wave Propagation M I Belishev 340
Boundary-Value Problems for Integrable Equations B Pelloni 346
Braided and Modular Tensor Categories V Lyubashenko 351
Brane Construction of Gauge Theories S L Cacciatori 360
Brane Worlds R Maartens 367
Branes and Black Hole Statistical Mechanics S R Das 373
Breaking Water Waves A Constantin 383
BRST Quantization M Henneaux 386
C
C
-Algebras and their Classification G A Elliott 393
Calibrated Geometry and Special Lagrangian Submanifolds D D Joyce 398
Calogero–Moser–Sutherland Systems of Nonrelativistic and Relativistic Type S N M Ruijsenaars 403
Canonical General Relativity C Rovelli 412
Capacities Enhanced by Entanglement P Hayden 418
Capacity for Quantum Information D Kretschmann 424
Capillary Surfaces R Finn 431
Cartan Model see Equivariant Cohomology and the Cartan Model
Cauchy Problem for Burgers-Type Equations G M Henkin 446
Cellular Automata M Bruschi and F Musso 455
Central Manifolds, Normal Forms P Bonckaert 467
Channels in Quantum Information Theory M Keyl 472
Chaos and Attractors R Gilmore 477
Characteristic Classes P B Gilkey, R Ivanova and S Nikc
ˇ
evic
´
488
Chern–Simons Models: Rigorous Results A N Sengupta 496
Classical Groups and Homogeneous Spaces S Gindikin 500
Classical r-Matrices, Lie Bialgebras, and Poisson Lie Groups M A Semenov-Tian-Shansky 511
Clifford Algebras and Their Representations A Trautman 518
Cluster Expansion R Kotecky
´
531
Coherent States S T Ali 537
Cohomology Theories U Tillmann 545
Combinatorics: Overview C Krattenthaler 553
Compact Groups and Their Representations A Kirillov and A Kirillov, Jr. 576
Compactification of Superstring Theory M R Douglas 586
Compressible Flows: Mathematical Theory G-Q Chen 595
Computational Methods in General Relativity: The Theory M W Choptuik 604
xl CONTENTS
Confinement see Quantum Chromodynamics
Conformal Geometry see Two-dimensional Conformal Field Theory and Vertex Operator Algebras
Conservation Laws see Symmetries and Conservation Laws
Constrained Systems M Henneaux 611
Constructive Quantum Field Theory G Gallavotti 617
Contact Manifolds J B Etnyre 631
Control Problems in Mathematical Physics B Piccoli 636
Convex Analysis and Duality Methods G Bouchitte
´
642
Cosmic Censorship see Spacetime Topology, Causal Structure and Singularities
Cosmology: Mathematical Aspects G F R Ellis 653
Cotangent Bundle Reduction J-P Ortega and T S Ratiu 658
Critical Phenomena in Gravitational Collapse C Gundlach 668
Current Algebra G A Goldin 674
VOLUME 2
D
Deformation Quantization A C Hirshfeld 1
Deformation Quantization and Representation Theory S Waldmann 9
Deformation Theory M J Pflaum 16
Deformations of the Poisson Bracket on a Symplectic Manifold S Gutt and S Waldmann 24
@-Approach to Integrable Systems P G Grinevich 34
Derived Categories E R Sharpe 41
Determinantal Random Fields A Soshnikov 47
Diagrammatic Techniques in Perturbation Theory G Gentile 54
Dimer Problems R Kenyon 61
Dirac Fields in Gravitation and Nonabelian Gauge Theory J A Smoller 67
Dirac Operator and Dirac Field S N M Ruijsenaars 74
Dispersion Relations J Bros 87
Dissipative Dynamical Systems of Infinite Dimension M Efendiev, S Zelik and A Miranville 101
Donaldson Invariants see Gauge Theoretic Invariants of 4-Manifolds
Donaldson–Witten Theory M Marin
˜
o 110
Duality in Topological Quantum Field Theory C Lozano and J M F Labastida 118
Dynamical Systems and Thermodynamics A Carati, L Galgani and A Giorgilli 125
Dynamical Systems in Mathematical Physics: An Illustration from Water Waves O Goubet 133
E
Effective Field Theories G Ecker 139
Eigenfunctions of Quantum Completely Integrable Systems J A Toth 148
Eight Vertex and Hard Hexagon Models P A Pearce 155
Einstein Equations: Exact Solutions Jir
ˇ
ı
´
Bic
ˇ
a
´
k 165
Einstein Equations: Initial Value Formulation J Isenberg 173
Einstein Manifolds A S Dancer 182
Einstein–Cartan Theory A Trautman 189
Einstein’s Equations with Matter Y Choquet-Bruhat 195
Electric–Magnetic Duality Tsou Sheung Tsun 201
Electroweak Theory K Konishi 209
Elliptic Differential Equations: Linear Theory C Amrouche, M Krbec, S
ˇ
Nec
ˇ
asova
´
and B Lucquin-Desreux 216
Entanglement R F Werner 228
CONTENTS xli
Entanglement Measures R F Werner 233
Entropy and Quantitative Transversality G Comte 237
Equivariant Cohomology and the Cartan Model E Meinrenken 242
Ergodic Theory M Yuri 250
Euclidean Field Theory F Guerra 256
Evolution Equations: Linear and Nonlinear J Escher 265
Exact Renormalization Group P K Mitter 272
F
Falicov–Kimball Model Ch Gruber and D Ueltschi 283
Fedosov Quantization N Neumaier 291
Feigenbaum Phenomenon see Universality and Renormalization
Fermionic Systems V Mastropietro 300
Feynman Path Integrals S Mazzucchi 307
Finite-Dimensional Algebras and Quivers A Savage 313
Finite Group Symmetry Breaking G Gaeta 322
Finite Weyl Systems D-M Schlingemann 328
Finitely Correlated States R F Werner 334
Finite-Type Invariants D Bar-Natan 340
Finite-Type Invariants of 3-Manifolds TTQLe
ˆ
348
Floer Homology P B Kronheimer 356
Fluid Mechanics: Numerical Methods J-L Guermond 365
Fourier Law F Bonetto and L Rey-Bellet 374
Fourier–Mukai Transform in String Theory B Andreas 379
Four-Manifold Invariants and Physics C Nash 386
Fractal Dimensions in Dynamics VZ
ˇ
upanovic
´
and D Z
ˇ
ubrinic
´
394
Fractional Quantum Hall Effect J K Jain 402
Free Interfaces and Free Discontinuities: Variational Problems G Buttazzo 411
Free Probability Theory D-V Voiculescu 417
Frobenius Manifolds see WDVV Equations and Frobenius Manifolds
Functional Equations and Integrable Systems H W Braden 425
Functional Integration in Quantum Physics C DeWitt-Morette 434
G
-Convergence and Homogenization G Dal Maso 449
Gauge Theoretic Invariants of 4-Manifolds S Bauer 457
Gauge Theories from Strings P Di Vecchia 463
Gauge Theory: Mathematical Applications S K Donaldson 468
General Relativity: Experimental Tests C M Will 481
General Relativity: Overview R Penrose 487
Generic Properties of Dynamical Systems C Bonatti 494
Geometric Analysis and General Relativity L Andersson 502
Geometric Flows and the Penrose Inequality H Bray 510
Geometric Measure Theory G Alberti 520
Geometric Phases PLe
´
vay 528
Geophysical Dynamics M B Ziane 534
Gerbes in Quantum Field Theory J Mickelsson 539
xlii CONTENTS
Ginzburg–Landau Equation Y Morita 547
Glassy Disordered Systems: Dynamical Evolution S Franz 553
Graded Poisson Algebras A S Cattaneo, D Fiorenza and R Longoni 560
Gravitational Lensing J Wambsganss 567
Gravitational N-Body Problem (Classical) D C Heggie 575
Gravitational Waves G Gonza
´
lez and J Pullin 582
Growth Processes in Random Matrix Theory K Johansson 586
H
Hamiltonian Fluid Dynamics P J Morrison 593
Hamiltonian Group Actions L C Jeffrey 600
Hamiltonian Reduction of Einstein’s Equations A E Fischer and V Moncrief 607
Hamiltonian Systems: Obstructions to Integrability M Irigoyen 624
Hamiltonian Systems: Stability and Instability Theory P Bernard 631
Hamilton–Jacobi Equations and Dynamical Systems: Variational Aspects A Siconolfi 636
Hard Hexagon Model see Eight Vertex and Hard Hexagon Models
High T
c
Superconductor Theory S-C Zhang 645
Holomorphic Dynamics M Lyubich 652
Holonomic Quantum Fields J Palmer 660
Homeomorphisms and Diffeomorphisms of the Circle A Zumpano and A Sarmiento 665
Homoclinic Phenomena S E Newhouse 672
Hopf Algebra Structure of Renormalizable Quantum Field Theory D Kreimer 678
Hopf Algebras and q-Deformation Quantum Groups S Majid 687
h-Pseudodifferential Operators and Applications B Helffer 701
Hubbard Model H Tasaki 712
Hydrodynamic Equations see Interacting Particle Systems and Hydrodynamic Equations
Hyperbolic Billiards M P Wojtkowski 716
Hyperbolic Dynamical Systems B Hasselblatt 721
VOLUME 3
I
Image Processing: Mathematics G Aubert and P Kornprobst 1
Incompressible Euler Equations: Mathematical Theory D Chae 10
Indefinite Metric H Gottschalk 17
Index Theorems P B Gilkey, K Kirsten, R Ivanova and J H Park 23
Inequalities in Sobolev Spaces M Vaugon 32
Infinite-Dimensional Hamiltonian Systems R Schmid 37
Instantons: Topological Aspects M Jardim 44
Integrability and Quantum Field Theory T J Hollowood 50
Integrable Discrete Systems O Ragnisco 59
Integrable Systems and Algebraic Geometry E Previato 65
Integrable Systems and Discrete Geometry A Doliwa and P M Santini 78
Integrable Systems and Recursion Operators on Symplectic and Jacobi Manifolds R Caseiro and
J M Nunes da Costa 87
Integrable Systems and the Inverse Scattering Method A S Fokas 93
Integrable Systems in Random Matrix Theory C A Tracy and H Widom 102
Integrable Systems: Overview Francesco Calogero 106
CONTENTS xliii
Interacting Particle Systems and Hydrodynamic Equations C Landim 123
Interacting Stochastic Particle Systems H Spohn 130
Interfaces and Multicomponent Fluids J Kim and J Lowengrub 135
Intermittency in Turbulence J Jime
´
nez 144
Intersection Theory A Kresch 151
Inverse Problem in Classical Mechanics R G Novikov 156
Inverse Problems in Wave Propagation see Boundary Control Method and Inverse Problems of Wave
Propagation
Inviscid Flows R Robert 160
Ising Model see Two-Dimensional Ising Model
Isochronous Systems Francesco Calogero 166
Isomonodromic Deformations V P Kostov 173
J
The Jones Polynomial V F R Jones 179
K
Kac–Moody Lie Algebras see Solitons and Kac–Moody Lie Algebras
KAM Theory and Celestial Mechanics L Chierchia 189
Kinetic Equations C Bardos 200
Knot Homologies J Rasmussen 208
Knot Invariants and Quantum Gravity R Gambini and J Pullin 215
Knot Theory and Physics L H Kauffman 220
Kontsevich Integral S Chmutov and S Duzhin 231
Korteweg–de Vries Equation and Other Modulation Equations G Schneider and E Wayne 239
K-Theory V Mathai 246
L
Lagrangian Dispersion (Passive Scalar) G Falkovich 255
Large Deviations in Equilibrium Statistical Mechanics S Shlosman 261
Large-N and Topological Strings R Gopakumar 263
Large-N Dualities A Grassi 269
Lattice Gauge Theory A Di Giacomo 275
Leray–Schauder Theory and Mapping Degree J Mawhin 281
Lie Bialgebras see Classical r-Matrices, Lie Bialgebras, and Poisson Lie Groups
Lie Groups: General Theory R Gilmore 286
Lie Superalgebras and Their Representations L Frappat 305
Lie, Symplectic, and Poisson Groupoids and Their Lie Algebroids C-M Marle 312
Liquid Crystals O D Lavrentovich 320
Ljusternik–Schnirelman Theory J Mawhin 328
Localization for Quasiperiodic Potentials S Jitomirskaya 333
Loop Quantum Gravity C Rovelli 339
Lorentzian Geometry P E Ehrlich and S B Kim 343
Lyapunov Exponents and Strange Attractors M Viana 349
M
Macroscopic Fluctuations and Thermodynamic Functionals G Jona-Lasinio 357
Magnetic Resonance Imaging C L Epstein and F W Wehrli 367
Magnetohydrodynamics C Le Bris 375
xliv CONTENTS