数学物理百科全书目录
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 Stringari312
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
Elli ptic 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-Lasinio357
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 Remiddi168 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′ ski236 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 Kozitsky376 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 Salmhofer407 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