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《数学物理学百科全书》.(Encyclopedia.of.Mathematical.Physics).Francoise,Gregory.L.Naber,Tsou.Sheung.文字版.PDF.pdf
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    目录:

    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 Nikcˇevic′ 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 Jirˇ?′ Bicˇa′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, SˇNecˇasova′ 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 T T Q Le? 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 V Zˇ upanovic′ and D Zˇ 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 P Le′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 Tc 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

    Malliavin Calculus A B Cruzeiro 383

    Marsden–Weinstein Reduction see Cotangent Bundle Reduction: Poisson Reduction: Symmetry and Symplectic Reduction

    Maslov Index see Optical Caustics: Semiclassical Spectra and ClosedOrbits: Stationary Phase Approximation

    Mathai–Quillen Formalism S Wu 390

    Mathematical Knot Theory L Boi 399

    Matrix Product States see Finitely Correlated States

    Mean Curvature Flow see Geometric Flows and the Penrose Inequality

    Mean Field Spin Glasses and Neural Networks A Bovier 407

    Measure on Loop Spaces H Airault 413

    Metastable States S Shlosman 417

    Minimal Submanifolds T H Colding and W P Minicozzi II 420

    Minimax Principle in the Calculus of Variations A Abbondandolo 432

    Mirror Symmetry: A Geometric Survey R P Thomas 439

    Modular Tensor Categories see Braided and Modular Tensor Categories

    Moduli Spaces: An Introduction F Kirwan 449

    Multicomponent Fluids see Interfaces and Multicomponent Fluids

    Multi-Hamiltonian Systems F Magri and M Pedroni 459

    Multiscale Approaches A Lesne 465

    N

    Negative Refraction and Subdiffraction Imaging S O’Brien and S A Ramakrishna 483

    Newtonian Fluids and Thermohydraulics G Labrosse and G Kasperski 492

    Newtonian Limit of General Relativity J Ehlers 503

    Noncommutative Geometry and the Standard Model T Schu¨cker 509

    Noncommutative Geometry from Strings Chong-Sun Chu 515

    Noncommutative Tori, Yang–Mills, and String Theory A Konechny 524

    Nonequilibrium Statistical Mechanics (Stationary): Overview G Gallavotti 530

    Nonequilibrium Statistical Mechanics: Dynamical Systems Approach P Butta` and C Marchioro 540

    Nonequilibrium Statistical Mechanics: Interaction between Theory and Numerical Simulations R Livi 544

    Nonlinear Schro¨dinger Equations M J Ablowitz and B Prinari 552

    Non-Newtonian Fluids C Guillope′ 560

    Nonperturbative and Topological Aspects of Gauge Theory R W Jackiw 568

    Normal Forms and Semiclassical Approximation D Bambusi 578

    N-Particle Quantum Scattering D R Yafaev 585

    Nuclear Magnetic Resonance P T Callaghan 592

    Number Theory in Physics M Marcolli 600

    O

    Operads J Stasheff 609

    Operator Product Expansion in Quantum Field Theory H Osborn 616

    Optical Caustics A Joets 620

    Optimal Cloning of Quantum States M Keyl 628

    Optimal Transportation Y Brenier 632

    Ordinary Special Functions W Van Assche 637

    CONTENTS xlv

    VOLUME 4

    P

    Painleve′ Equations N Joshi 1

    Partial Differential Equations: Some Examples R Temam 6

    Path Integral Methods see Functional Integration in Quantum Physics; Feynman Path Integrals

    Path Integrals in Noncommutative Geometry R Le′andre 8

    Peakons D D Holm 12

    Penrose Inequality see Geometric Flows and the Penrose Inequality

    Percolation Theory V Beffara and V Sidoravicius 21

    Perturbation Theory and Its Techniques R J Szabo 28

    Perturbative Renormalization Theory and BRST K Fredenhagen and M Du¨tsch 41

    Phase Transition Dynamics A Onuki 47

    Phase Transitions in Continuous Systems E Presutti 53

    Pirogov–Sinai Theory R Kotecky′ 60

    Point-Vortex Dynamics S Boatto and D Crowdy 66

    Poisson Lie Groups see Classical r-Matrices, Lie Bialgebras, and Poisson Lie Groups

    Poisson Reduction J-P Ortega and T S Ratiu 79

    Polygonal Billiards S Tabachnikov 84

    Positive Maps on C-Algebras F Cipriani 88

    Pseudo-Riemannian Nilpotent Lie Groups P E Parker 94

    Q

    q-Special Functions T H Koornwinder 105

    Quantum 3-Manifold Invariants C Blanchet and V Turaev 117

    Quantum Calogero–Moser Systems R Sasaki 123

    Quantum Central-Limit Theorems A F Verbeure 130

    Quantum Channels: Classical Capacity A S Holevo 142

    Quantum Chromodynamics G Sterman 144

    Quantum Cosmology M Bojowald 153

    Quantum Dynamical Semigroups R Alicki 159

    Quantum Dynamics in Loop Quantum Gravity H Sahlmann 165

    Quantum Electrodynamics and Its Precision Tests S Laporta and E Remiddi

    168

    Quantum Entropy D Petz 177

    Quantum Ergodicity and Mixing of Eigenfunctions S Zelditch 183

    Quantum Error Correction and Fault Tolerance D Gottesman 196

    Quantum Field Theory in Curved Spacetime B S Kay 202

    Quantum Field Theory: A Brief Introduction L H Ryder 212

    Quantum Fields with Indefinite Metric: Non-Trivial Models S Albeverio and H Gottschalk 216

    Quantum Fields with Topological Defects M Blasone, G Vitiello and P Jizba 221

    Quantum Geometry and Its Applications A Ashtekar and J Lewandowski 230

    Quantum Group Differentials, Bundles and Gauge Theory T Brzezin′ ski

    236

    Quantum Hall Effect K Hannabuss 244

    Quantum Mechanical Scattering Theory D R Yafaev 251

    Quantum Mechanics: Foundations R Penrose 260

    Quantum Mechanics: Generalizations P Pearle and A Valentini 265

    Quantum Mechanics: Weak Measurements L Dio′ si 276

    Quantum n-Body Problem R G Littlejohn 283

    xlvi CONTENTS

    Quantum Phase Transitions S Sachdev 289

    Quantum Spin Systems B Nachtergaele 295

    Quantum Statistical Mechanics: Overview L Triolo 302

    Quasiperiodic Systems P Kramer 308

    Quillen Determinant S Scott 315

    Quivers see Finite-Dimensional Algebras and Quivers

    R

    Random Algebraic Geometry, Attractors and Flux Vacua M R Douglas 323

    Random Dynamical Systems V Arau′ jo 330

    Random Matrix Theory in Physics T Guhr 338

    Random Partitions A Okounkov 347

    Random Walks in Random Environments L V Bogachev 353

    Recursion Operators in Classical Mechanics F Magri and M Pedroni 371

    Reflection Positivity and Phase Transitions Y Kondratiev and Y Kozitsky

    376

    Regularization for Dynamical -Functions V Baladi 386

    Relativistic Wave Equations Including Higher Spin Fields R Illge and V Wu¨nsch 391

    Renormalization: General Theory J C Collins 399

    Renormalization: Statistical Mechanics and Condensed Matter M Salmhofer

    407

    Resonances N Burq 415

    Ricci Flow see Singularities of the Ricci Flow

    Riemann Surfaces K Hulek 419

    Riemann–Hilbert Methods in Integrable Systems D Shepelsky 429

    Riemann–Hilbert Problem V P Kostov 436

    Riemannian Holonomy Groups and Exceptional Holonomy D D Joyce 441

    S

    Saddle Point Problems M Schechter 447

    Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools D Buchholz and S J Summers 456

    Scattering in Relativistic Quantum Field Theory: The Analytic Program J Bros 465

    Scattering, Asymptotic Completeness and Bound States D Iagolnitzer and J Magnen 475

    Schro¨dinger Operators V Bach 487

    Schwarz-Type Topological Quantum Field Theory R K Kaul, T RGovindarajan and P Ramadevi 494

    Seiberg–Witten Theory Siye Wu 503

    Semiclassical Approximation see Stationary Phase Approximation; Normal Forms and

    Semiclassical Approximation

    Semiclassical Spectra and Closed Orbits Y Colin de Verdie`re 512

    Semilinear Wave Equations P D’Ancona 518

    Separation of Variables for Differential Equations S Rauch-Wojciechowski and K Marciniak 526

    Separatrix Splitting D Treschev 535

    Several Complex Variables: Basic Geometric Theory A Huckleberry and T Peternell 540

    Several Complex Variables: Compact Manifolds A Huckleberry and T Peternell 551

    Shock Wave Refinement of the Friedman–Robertson–Walker Metric B Temple and J Smoller 559

    Shock Waves see Symmetric Hyperbolic Systems and Shock Waves

    Short-Range Spin Glasses: The Metastate Approach C M Newman and D L Stein 570

    Sine-Gordon Equation S N M Ruijsenaars 576

    Singularities of the Ricci Flow M Anderson 584

    Singularity and Bifurcation Theory J-P Franc? oise and C Piquet 588

    CONTENTS xlvii

    Sobolev Spaces see Inequalities in Sobolev Spaces

    Solitons and Kac–Moody Lie Algebras E Date 594

    Solitons and Other Extended Field Configurations R S Ward 602

    Source Coding in Quantum Information Theory N Datta and T C Dorlas 609

    Spacetime Topology, Causal Structure and Singularities R Penrose 617

    Special Lagrangian Submanifolds see Calibrated Geometry and Special Lagrangian Submanifolds

    Spectral Sequences P Selick 623

    Spectral Theory of Linear Operators M Schechter 633

    Spin Foams A Perez 645

    Spin Glasses F Guerra 655

    Spinors and Spin Coefficients K P Tod 667

    VOLUME 5

    Stability of Flows S Friedlander 1

    Stability of Matter J P Solovej 8

    Stability of Minkowski Space S Klainerman 14

    Stability Problems in Celestial Mechanics A Celletti 20

    Stability Theory and KAM G Gentile 26

    Standard Model of Particle Physics G Altarelli 32

    Stationary Black Holes R Beig and P T Chrus′ciel 38

    Stationary Phase Approximation J J Duistermaat 44

    Statistical Mechanics and Combinatorial Problems R Zecchina 50

    Statistical Mechanics of Interfaces S Miracle-Sole′ 55

    Stochastic Differential Equations F Russo 63

    Stochastic Hydrodynamics B Ferrario 71

    Stochastic Loewner Evolutions G F Lawler 80

    Stochastic Resonance S Herrmann and P Imkeller 86

    Strange Attractors see Lyapunov Exponents and Strange Attractors

    String Field Theory L Rastelli 94

    String Theory: Phenomenology A M Uranga 103

    String Topology: Homotopy and Geometric Perspectives R L Cohen 111

    Superfluids D Einzel 115

    Supergravity K S Stelle 122

    Supermanifolds F A Rogers 128

    Superstring Theories C Bachas and J Troost 133

    Supersymmetric Particle Models S Pokorski 140

    Supersymmetric Quantum Mechanics J-W van Holten 145

    Supersymmetry Methods in Random Matrix Theory M R Zirnbauer 151

    Symmetric Hyperbolic Systems and Shock Waves S Kichenassamy 160

    Symmetries and Conservation Laws L H Ryder 166

    Symmetries in Quantum Field Theory of Lower Spacetime Dimensions J Mund and K-H Rehren 172

    Symmetries in Quantum Field Theory: Algebraic Aspects J E Roberts 179

    Symmetry and Symmetry Breaking in Dynamical Systems I Melbourne 184

    Symmetry and Symplectic Reduction J-P Ortega and T S Ratiu 190

    Symmetry Breaking in Field Theory T W B Kibble 198

    Symmetry Classes in Random Matrix Theory M R Zirnbauer 204

    Synchronization of Chaos M A Aziz-Alaoui 213

    xlviii CONTENTS

    T

    t Hooft–Polyakov Monopoles see Solitons and Other Extended Field Configurations

    Thermal Quantum Field Theory C D Ja¨kel 227

    Thermohydraulics see Newtonian Fluids and Thermohydraulics

    Toda Lattices Y B Suris 235

    Toeplitz Determinants and Statistical Mechanics E L Basor 244

    Tomita–Takesaki Modular Theory S J Summers 251

    Topological Defects and Their Homotopy Classification T W B Kibble 257

    Topological Gravity, Two-Dimensional T Eguchi 264

    Topological Knot Theory and Macroscopic Physics L Boi 271

    Topological Quantum Field Theory: Overview J M F Labastida and C Lozano 278

    Topological Sigma Models D Birmingham 290

    Turbulence Theories R M S Rosa 295

    Twistor Theory: Some Applications L Mason 303

    Twistors K P Tod 311

    Two-Dimensional Conformal Field Theory and Vertex Operator Algebras M R Gaberdiel 317

    Two-Dimensional Ising Model B M McCoy 322

    Two-Dimensional Models B Schroer 328

    U

    Universality and Renormalization M Lyubich 343

    V

    Variational Methods in Turbulence F H Busse 351

    Variational Techniques for Ginzburg–Landau Energies S Serfaty 355

    Variational Techniques for Microstructures G Dolzmann 363

    Vertex Operator Algebras see Two-Dimensional Conformal Field Theory and Vertex

    Operator Algebras

    Viscous Incompressible Fluids: Mathematical Theory J G Heywood 369

    von Neumann Algebras: Introduction, Modular Theory, and Classification Theory V S Sunder 379

    von Neumann Algebras: Subfactor Theory Y Kawahigashi 385

    Vortex Dynamics M Nitsche 390

    Vortices see Abelian Higgs Vortices: Point-Vortex Dynamics

    W

    Wave Equations and Diffraction M E Taylor 401

    Wavelets: Application to Turbulence M Farge and K Schneider 408

    Wavelets: Applications M Yamada 420

    Wavelets: Mathematical Theory K Schneider and M Farge 426

    WDVV Equations and Frobenius Manifolds B Dubrovin 438

    Weakly Coupled Oscillators E M Izhikevich and Y Kuramoto 448

    Wheeler–De Witt Theory J Maharana 453

    Wightman Axioms see Axiomatic Quantum Field Theory

    Wulff Droplets S Shlosman 462

    Y

    Yang–Baxter Equations J H H Perk and H Au-Yang 465