Contents list by subject.pdf

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CONTENTS LIST BY SUBJECT
Location references refer to the volume number and page number (separated by a colon).
INTRODUCTORY ARTICLES
Donaldson–Witten Theory 2:110
Duality in Topological Quantum Field
Theory 2:118
Finite-Type Invariants 2:340
Four-Manifold Invariants and Physics 2:386
Gauge Theoretic Invariants of 4-Manifolds 2:457
h -Pseudodifferential Operators and
Applications 2:701
The Jones Polynomial 3:179
Knot Theory and Physics 3:220
Kontsevich Integral 3:231
Large- N and Topological Strings 3:263
Mathai–Quillen Formalism 3:390
Mathematical Knot Theory 3:399
Operator Product Expansion in Quantum Field
Theory 3:616
Schwarz-Type Topological Quantum Field
Theory 4:494
Solitons and Other Extended Field
Configurations 4:602
Topological Defects and Their Homotopy
Classification 5:257
Topological Gravity, Two-Dimensional 5:264
Topological Knot Theory and Macroscopic
Physics 5:271
Topological Sigma Models 5:290
Two-Dimensional Conformal Field Theory and
Vertex Operator Algebras 5:317
WDVV Equations and Frobenius
Manifolds 5:438
Classical Mechanics 1:1
Differential Geometry 1:33
Electromagnetism 1:40
Equilibrium Statistical Mechanics 1:51
Functional Analysis 1:88
Minkowski Spacetime and Special Relativity 1:96
Quantum Mechanics 1:109
Topology 1:131
PHYSICS SUBJECTS
Classical Mechanics
Boundary Control Method and Inverse Problems of
Wave Propagation 1:340
Constrained Systems 1:611
Cotangent Bundle Reduction 1:658
Gravitational N -body Problem (Classical) 2:575
Hamiltonian Fluid Dynamics 2:593
Hamiltonian Systems: Obstructions to
Integrability 2:624
Infinite-Dimensional Hamiltonian Systems 3:37
Inverse Problem in Classical Mechanics 3:156
KAM Theory and Celestial Mechanics 3:189
Peakons 4:12
Poisson Reduction 4:79
Stability Problems in Celestial Mechanics 5:20
Symmetry and Symplectic Reduction 5:190
Classical, Conformal and Topological
Field Theory
Topological Quantum Field Theory:
Overview 5:278
AdS/CFT Correspondence 1:174
Axiomatic Approach to Topological Quantum Field
Theory 1:232
BF Theories 1:257
Boundary Conformal Field Theory 1:333
Chern–Simons Models: Rigorous Results 1:496
Condensed Matter and Optics
Bose–Einstein Condensates 1:312
Falicov–Kimball Model 2:283
Fractional Quantum Hall Effect 2:402
High T c Superconductor Theory 2:645
Hubbard Model 2:712
Liquid Crystals 3:320
Negative Refraction and Subdiffraction
Imaging 3:483
Nuclear Magnetic Resonance 3:592
xxxii CONTENTS LIST BY SUBJECT
Optical Caustics 3:620
Quantum Phase Transitions 4:289
Quasiperiodic Systems 4:308
Renormalization: Statistical Mechanics and
Condensed Matter 4:407
Short-Range Spin Glasses: The Metastate
Approach 4:570
Topological Defects and Their Homotopy
Classification 5:257
KAM Theory and Celestial Mechanics 3:189
Lyapunov Exponents and Strange Attractors 3:349
Multiscale Approaches 3:465
Normal Forms and Semiclassical
Approximation 3:578
Point-Vortex Dynamics 4:66
Poisson Reduction 4:79
Polygonal Billiards 4:84
Quasiperiodic Systems 4:308
Random Dynamical Systems 4:330
Regularization For Dynamical -Functions 4:386
Resonances 4:415
Riemann–Hilbert Problem 4:436
Semiclassical Spectra and Closed Orbits 4:512
Separatrix Splitting 4:535
Stability Problems in Celestial Mechanics 5:20
Stability Theory and KAM 5:26
Symmetry and Symmetry Breaking in Dynamical
Systems 5:184
Symmetry and Symplectic Reduction 5:190
Synchronization of Chaos 5:213
Universality and Renormalization 5:343
Weakly Coupled Oscillators 5:448
Disordered Systems
Cellular Automata 1:455
Lagrangian Dispersion (Passive Scalar) 3:255
Mean Field Spin Glasses and Neural
Networks 3:407
Percolation Theory 4:21
Random Matrix Theory in Physics 4:338
Random Walks in Random Environments 4:353
Short-Range Spin Glasses: The Metastate
Approach 4:570
Spin Glasses 4:655
Stochastic Loewner Evolutions 5:80
Two-Dimensional Ising Model 5:322
Wulff Droplets 5:462
Equilibrium Statistical Mechanics
Bethe Ansatz 1:253
Cluster Expansion 1:531
Dimer Problems 2:61
Eight Vertex and Hard Hexagon Models 2:155
Falicov–Kimball Model 2:283
Fermionic Systems 2:300
Finitely Correlated States 2:334
Holonomic Quantum Fields 2:660
Hubbard Model 2:712
Large Deviations in Equilibrium Statistical
Mechanics 3:261
Metastable States 3:417
Phase Transitions in Continuous Systems 4:53
Pirogov–Sinai Theory 4:60
Quantum Central-Limit Theorems 4:130
Quantum Phase Transitions 4:289
Quantum Spin Systems 4:295
Quantum Statistical Mechanics: Overview 4:302
Reflection Positivity and Phase Transitions 4:376
Short-Range Spin Glasses: The Metastate
Approach 4:570
Statistical Mechanics and Combinatorial
Problems 5:50
Statistical Mechanics of Interfaces 5:55
Superfluids 5:115
Toeplitz Determinants and Statistical
Mechanics 5:244
Two-Dimensional Ising Model 5:322
Wulff Droplets 5:462
Dynamical Systems
Averaging Methods 1:226
Bifurcations of Periodic Orbits 1:285
Billiards in Bounded Convex Domains 1:296
Central Manifolds, Normal Forms 1:467
Cellular Automata 1:455
Chaos and Attractors 1:477
Cotangent Bundle Reduction 1:658
Diagrammatic Techniques in Perturbation
Theory 2:54
Dissipative Dynamical Systems of Infinite
Dimension 2:101
Dynamical Systems and Thermodynamics 2:125
Dynamical Systems in Mathematical Physics:
An Illustration from Water Waves 2:133
Entropy and Quantitative Transversality 2:237
Ergodic Theory 2:250
Fractal Dimensions in Dynamics 2:394
Generic Properties of Dynamical Systems 2:494
Gravitational N -Body Problem (Classical) 2:575
Hamiltonian Fluid Dynamics 2:593
Hamiltonian Systems: Stability and Instability
Theory 2:631
Holomorphic Dynamics 2:652
Homeomorphisms and Diffeomorphisms of the
Circle 2:665
Homoclinic Phenomena 2:672
h -Pseudodifferential Operators and
Applications 2:701
Hyperbolic Billiards 2:716
Hyperbolic Dynamical Systems 2:721
Isomonodromic Deformations 3:173
Fluid Dynamics
Bifurcations in Fluid Dynamics 1:281
Breaking Water Waves 1:383
CONTENTS LIST BY SUBJECT xxxiii
Capillary Surfaces 1:431
Cauchy Problem for Burgers-Type Equations 1:446
Compressible Flows: Mathematical Theory 1:595
Fluid Mechanics: Numerical Methods 2:365
Geophysical Dynamics 2:534
Hamiltonian Fluid Dynamics 2:593
Incompressible Euler Equations: Mathematical
Theory 3:10
Interfaces and Multicomponent Fluids 3:135
Intermittency in Turbulence 3:144
Inviscid Flows 3:160
Korteweg–de Vries Equation and Other Modulation
Equations 3:239
Lagrangian Dispersion (Passive Scalar) 3:255
Magnetohydrodynamics 3:375
Newtonian Fluids and Thermohydraulics 3:492
Non-Newtonian Fluids 3:560
Partial Differential Equations: Some Examples 4:6
Peakons 4:12
Stability of Flows 5:1
Superfluids 5:115
Turbulence Theories 5:295
Variational Methods in Turbulence 5:351
Viscous Incompressible Fluids: Mathematical
Theory 5:369
Vortex Dynamics 5:390
Wavelets: Application to Turbulence 5:408
Renormalization: General Theory 4:399
Seiberg–Witten Theory 4:503
Standard Model of Particle Physics 5:32
Supergravity 5:122
Supersymmetric Particle Models 5:140
Symmetry Breaking in Field Theory 5:198
Twistor Theory: Some Applications 5:303
Two-Dimensional Models 5:328
General Relativity
General Relativity: Overview 2:487
Asymptotic Structure and Conformal
Infinity 1:221
Black Hole Mechanics 1:300
Boundaries for Spacetimes 1:326
Brane Worlds 1:367
Canonical General Relativity 1:412
Critical Phenomena in Gravitational
Collapse 1:668
Computational Methods in General Relativity:
The Theory 1:604
Cosmology: Mathematical Aspects 1:653
Dirac Fields in Gravitation and Nonabelian Gauge
Theory 2:67
Einstein–Cartan Theory 2:189
Einstein’s Equations with Matter 2:195
Einstein Equations: Exact Solutions 2:165
Einstein Equations: Initial Value
Formulation 2:173
General Relativity: Experimental Tests 2:481
Geometric Analysis and General Relativity 2:502
Geometric Flows and the Penrose
Inequality 2:510
Gravitational Lensing 2:567
Gravitational Waves 2:582
Hamiltonian Reduction of Einstein’s
Equations 2:607
Minimal Submanifolds 3:420
Newtonian Limit of General Relativity 3:503
Quantum Field Theory in Curved
Spacetime 4:202
Relativistic Wave Equations Including Higher Spin
Fields 4:391
Shock Wave Refinement of the Friedman–
Robertson–Walker Metric 4:559
Spacetime Topology, Causal Structure and
Singularities 4:617
Spinors and Spin Coefficients 4:667
Stability of Minkowski Space 5:14
Stationary Black Holes 5:38
Twistors 5:311
Gauge Theory
Abelian and Nonabelian Gauge Theories Using
Differential Forms 1:141
Abelian Higgs Vortices 1:151
AdS/CFT Correspondence 1:174
Aharonov–Bohm Effect 1:191
Anomalies 1:205
BRST Quantization 1:386
Chern–Simons Models: Rigorous Results 1:496
Dirac Fields in Gravitation and Nonabelian Gauge
Theory 2:67
Donaldson–Witten Theory 2:110
Effective Field Theories 2:139
Electric–Magnetic Duality 2:201
Electroweak Theory 2:209
Exact Renormalization Group 2:272
Gauge Theories from Strings 2:463
Gauge Theory: Mathematical Applications 2:468
Instantons: Topological Aspects 3:44
Large- N and Topological Strings 3:263
Lattice Gauge Theory 3:275
Measure on Loop Spaces 3:413
Noncommutative Geometry and the Standard
Model 3:509
Nonperturbative and Topological Aspects of Gauge
Theory 3:568
Perturbative Renormalization Theory and
BRST 4:41
Quantum Chromodynamics 4:144
Quantum Electrodynamics and Its Precision
Tests 4:168
Integrable Systems
Integrable Systems: Overview 3:106
Abelian Higgs Vortices 1:151
Affine Quantum Groups 1:183
B¨ cklund Transformations 1:241
xxxiv CONTENTS LIST BY SUBJECT
Bethe Ansatz 1:253
Bi-Hamiltonian Methods in Soliton Theory 1:290
Boundary-Value Problems For Integrable
Equations 1:346
Calogero–Moser–Sutherland Systems of
Nonrelativistic and Relativistic Type 1:403
-Approach to Integrable Systems 2:34
Eigenfunctions of Quantum Completely Integrable
Systems 2:148
Functional Equations and Integrable Systems 2:425
Holonomic Quantum Fields 2:660
Instantons: Topological Aspects 3:44
Integrability and Quantum Field Theory 3:50
Integrable Discrete Systems 3:59
Integrable Systems and Algebraic Geometry 3:65
Integrable Systems and Discrete Geometry 3:78
Integrable Systems and Recursion Operators on
Symplectic and Jacobi Manifolds 3:87
Integrable Systems and the Inverse Scattering
Method 3:93
Integrable Systems in Random Matrix
Theory 3:102
Isochronous Systems 3:166
Nonlinear Schr¨ dinger Equations 3:552
Painlev´ Equations 4:1
Peakons 4:12
Quantum Calogero–Moser Systems 4:123
Riemann–Hilbert Methods in Integrable
Systems 4:429
Sine-Gordon Equation 4:576
Solitons and Kac–Moody Lie Algebras 4:594
Toda Lattices 5:235
Twistor Theory: Some Applications 5:303
Yang–Baxter Equations 5:465
Phase Transition Dynamics 4:47
Stochastic Resonance 5:86
Quantum Field Theory
Quantum Field Theory: A Brief
Introduction 4:212
AdS/CFT Correspondence 1:174
Algebraic Approach to Quantum Field
Theory 1:198
Anomalies 1:205
Axiomatic Quantum Field Theory 1:234
Batalin–Vilkovisky Quantization 1:247
Bosons and Fermions in External Fields 1:318
BRST Quantization 1:386
Constrained Systems 1:611
Constructive Quantum Field Theory 1:617
Current Algebra 1:674
Dirac Operator and Dirac Field 2:74
Dispersion Relations 2:87
Effective Field Theories 2:139
Electroweak Theory 2:209
Euclidean Field Theory 2:256
Exact Renormalization Group 2:272
Gerbes in Quantum Field Theory 2:539
Holonomic Quantum Fields 2:660
Hopf Algebra Structure of Renormalizable
Quantum Field Theory 2:678
Indefinite Metric 3:17
Integrability and Quantum Field Theory 3:50
Large- N and Topological Strings 3:263
Nonperturbative and Topological Aspects of Gauge
Theory 3:568
Operator Product Expansion in Quantum Field
Theory 3:616
Quantum Fields with Indefinite Metric: Non-Trivial
Models 4:216
Perturbation Theory and Its Techniques 4:28
Perturbative Renormalization Theory and
BRST 4:41
Quantum Electrodynamics and Its Precision
Tests 4:168
Quantum Fields with Topological Defects 4:221
Quantum Field Theory in Curved
Spacetime 4:202
Quantum Phase Transitions 4:289
Renormalization: General Theory 4:399
Renormalization: Statistical Mechanics and
Condensed Matter 4:407
Scattering, Asymptotic Completeness and Bound
States 4:475
Scattering in Relativistic Quantum Field Theory:
Fundamental Concepts and Tools 4:456
Scattering in Relativistic Quantum Field Theory:
The Analytic Program 4:465
Seiberg–Witten Theory 4:503
Standard Model of Particle Physics 5:32
Supergravity 5:122
Supersymmetric Particle Models 5:140
Symmetries and Conservation Laws 5:166
M-Theory see String Theory and
M-Theory
Nonequilibrium Statistical Mechanics
Nonequilibrium Statistical Mechanics (Stationary):
Overview 3:530
Adiabatic Piston 1:160
Boltzmann Equation (Classical and
Quantum) 1:306
Glassy Disordered Systems: Dynamical
Evolution 2:553
Fourier Law 2:374
Interacting Particle Systems and Hydrodynamic
Equations 3:123
Interacting Stochastic Particle Systems 3:130
Kinetic Equations 3:200
Macroscopic Fluctuations and Thermodynamic
Functionals 3:357
Nonequilibrium Statistical Mechanics: Dynamical
Systems Approach 3:540
Nonequilibrium Statistical Mechanics: Interaction
between Theory and Numerical
Simulations 3:544
CONTENTS LIST BY SUBJECT xxxv
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 Mechanics: Weak Measurements 4:276
Quantum n -Body Problem 4:283
Quantum Spin Systems 4:295
Quasiperiodic Systems 4:308
Schr¨ 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
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
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
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
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

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