Encyclopedia of mathematical physics, Volume 1

Front Cover
Elsevier, Jun 6, 2006 - Science - 3500 pages
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The Encyclopedia of Mathematical Physics provides a complete resource for researchers,
students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information.

* First comprehensive interdisciplinary coverage
* Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields
* Written by an international group of experts
* Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise
* Thematic index and extensive cross-referencing to provide easy access and quick search functionality
* Also available online with active linking.

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Contents

Location references refer to the volume number and page number separated by a colon
1
Algebraic Topology
2
Path Integral Methods see Functional Integration in Quantum Physics Feynman Path Integrals
7
Deformation Quantization and Representation Theory S Waldmann
9
PHYSICS SUBJECTS
12
Deformation Theory M J Pflaum
16
Penrose Inequality see Geometric Flows and the Penrose Inequality
21
Deformations of the Poisson Bracket on a Symplectic Manifold S Gutt and S Waldmann
24
Liquid Crystals O D Lavrentovich
320
Quivers see FiniteDimensional Algebras and Quivers
322
Boundaries for Spacetimes S G Harris
326
Finite Weyl Systems DM Schlingemann
328
Random Dynamical Systems V Araujo
330
Random Matrix Theory in Physics T Guhr
338
Loop Quantum Gravity C Rovelli
339
Boundary Control Method and Inverse Problems of Wave Propagation M I Belishev
340

Perturbation Theory and Its Techniques R J Szabo
28
Differential Geometry S Paycha
33
cApproach to Integrable Systems P G Grinevich
34
Electromagnetism N M J Woodhouse
40
Derived Categories E R Shame
41
Dynamical Systems
43
Determinantal Random Fields A Soshnikov
47
Equilibrium Statistical Mechanics G Gallavotti
51
Phase Transitions in Continuous Systems E Presutti
53
Diagrammatic Techniques in Perturbation Theory G Gentile
54
PirogovSinai Theory R Kotecky
60
Dimer Problems R Kenyon
61
PointVortex Dynamics S Boatto and D Crowdy
66
Dirac Fields in Gravitation and Nonabelian Gauge Theory J A Smoller
67
Dirac Operator and Dirac Field S N M Ruijsenaars
74
Poisson Lie Groups see Classical rMatrices Lie Bialgebras and Poisson Lie Groups
79
Malliavin Calculus A B Cruzeiro 383
80
Dispersion Relations J Bros
87
Functional Analysis S Paycha
88
Classical Conformal and Topological
93
PseudoRiemannian Nilpotent Lie Groups P E Parker
94
Minkowski Spacetime and Special Relativity G L Naber
96
Dissipative Dynamical Systems of Infinite Dimension M Efendiev S Zelik and A Miranville
101
gSpecial Functions T H Koornwinder
105
Quantum Mechanics G F dellAntonio
109
Donaldson Invariants see Gauge Theoretic Invariants of 4Manifolds
110
Quantum 3Manifold Invariants C Blanchet and V Turaev
117
Duality in Topological Quantum Field Theory C Lozano and J M F Labastida
118
Quantum Gravity
122
Interacting Particle Systems and Hydrodynamic Equations C Landim
123
Dynamical Systems and Thermodynamics A Carati L Galgani and A Giorgilli
125
Interacting Stochastic Particle Systems H Spohn
130
Topology Tsou Sheung Tsun
131
An Illustration from Water Waves O Goubet
133
Effective Field Theories G Ecker
139
Abelian and Nonabelian Gauge Theories Using Differential Forms A C Hirshfeld
141
Classical Capacity A S Holevo
142
Intermittency in Turbulence J Jimenez
144
Eigenfunctions of Quantum Completely Integrable Systems J A loth
148
Abelian Higgs Vortices J M Speight
151
Quantum Field Theory
152
Quantum Cosmology M Bojowald
153
Eight Vertex and Hard Hexagon Models PA Pearce
155
General Relativity
158
Quantum Dynamical Semigroups R Alicki
159
Adiabatic Piston Ch Gruber and A Lesne
160
Exact Solutions Jiff Bicak
165
Ising Model see TwoDimensional Ising Model
166
Initial Value Formulation J Isenberg
173
AdSCFT Correspondence C P Herzog and I R Klebanov
174
Quantum Information and Computation
177
The Jones Polynomial V F R Jones
179
Einstein Manifolds A S Dancer
182
Affine Quantum Groups G W Delius and N MacKay
183
EinsteinCartan Theory A Trautman
189
AharonovBohm Effect M Socolovsky
191
Einsteins Equations with Matter Y ChoquetBruhat
195
Quantum Error Correction and Fault Tolerance D Gottesman
196
Algebraic Approach to Quantum Field Theory F Brunetti and K Fredenhagen
198
Kinetic Equations C Bardos
200
ElectricMagnetic Duality Tsou Sheung Tsun
201
Quantum Field Theory in Curved Spacetime B S Kay
202
Anderson Localization see Localization for Quasiperiodic Potentials
205
Knot Homologies J Rasmussen
208
Electroweak Theory K Konishi
209
Arithmetic Quantum Chaos J Marklof
212
Knot Invariants and Quantum Gravity R Gambini and J Pullin
215
Linear Theory C Amrouche M Krbec S Necasova and B LucquinDesreux
216
Asymptotic Structure and Conformal Infinity J Frauendiener
221
Entanglement R F Werner
228
Quantum Geometry and Its Applications A Ashtekar and J Lewandowski
230
Kontsevich Integral S Chmutov and S Duzhin
231
Axiomatic Approach to Topological Quantum Field Theory C Blanchet and V Turaev
232
Entanglement Measures R F Werner
233
Thermohydraulics see Newtonian Fluids and Thermohydraulics
235
Quantum Group Differentials Bundles and Gauge Theory T Brzezihski
238
Kortewegde Vries Equation and Other Modulation Equations G Schneider and E Wayne
239
Backlund Transformations D Levi
241
Quantum Hall Effect K Hannabuss
244
Mathai
246
BatalinVilkovisky Quantization A C Hirshfeld
247
Ergodic Theory M Yuri
250
Quantum Mechanical Scattering Theory D R Yafaev
251
Bethe Ansatz M T Batchelor
253
Lagrangian Dispersion Passive Scalar G Falkovich
255
Ordinary and Partial Differential
256
Topological Defects and Their Homotopy Classification T W B Kibble
257
Foundations R Penrose
260
Large Deviations in Equilibrium Statistical Mechanics S Shlosman
261
Topological Gravity TwoDimensional T Eguchi
264
Complex Geometry
265
LargeV Dualities A Grassi
269
Topological Knot Theory and Macroscopic Physics L Boi
271
Bifurcation Theory M Haragus and G looss
275
Weak Measurements L Diosi
276
Overview J M F Labastida and C Lozano
278
LeraySchauder Theory and Mapping Degree J Mawhin
281
FalicovKimball Model Ch Gruber and D Ueltschi
283
Quantum Phase Transitions S Sachdev
289
BiHamiltonian Methods in Soliton Theory M Pedroni
290
Quantum Spin Systems B Nachtergaele
295
Feigenbaum Phenomenon see Universality and Renormalization
300
Overview L Triolo
302
Some Applications L Mason
303
Lie Superalgebras and Their Representations L Frappat
305
Boltzmann Equation Classical and Quantum M Pulvirenti
306
Quasiperiodic Systems P Kramer
308
Twistors KPTod
311
Lie Symplectic and Poisson Groupoids and Their Lie Algebroids CM Marie
312
FiniteDimensional Algebras and Quivers A Savage
313
Mathematical Applications 2468
315
TwoDimensional Conformal Field Theory and Vertex Operator Algebras M R Gaberdiel
317
Universality and Renormalization M Lyubich
343
Random Partitions A Okounkov
347
FiniteType Invariants of 3Manifolds T T O Le
348
Lyapunov Exponents and Strange Attractors M Viana
349
Variational Methods in Turbulence F H Busse
351
Random Walks in Random Environments L V Bogachev
353
Macroscopic Fluctuations and Thermodynamic Functionals G JonaLasinio
357
String Theory and WTheory
360
Variational Techniques for Microstructures G Dolzmann
363
Numerical Methods JL Guermond
365
Magnetic Resonance Imaging C L Epstein and F W Wehrli
367
Mathematical Theory J G Heywood
369
Recursion Operators in Classical Mechanics F Magri and M Pedroni
371
Branes and Black Hole Statistical Mechanics S R Das
373
Le Bris
375
FourierMukai Transform in String Theory B Andreas
379
Subfactor Theory Y Kawahigashi
385
BRST Quantization M Henneaux
386
MathaiQuillen Formalism S Wu
390
Fractal Dimensions in Dynamics V Zupanovic and D Zubrinic
394
Mathematical Knot Theory L Boi
399
CalogeroMoserSutherland Systems of Nonrelativistic and Relativistic Type S N M Ruijsenaars
403
Matrix Product States see Finitely Correlated States
407
Application to Turbulence M Farge and K Schneider
408
Variational Problems G Buttazzo
411
Measure on Loop Spaces H Airault
413
Resonances N Burq
415
Capacities Enhanced by Entanglement P Hayden
418
Minimal Submanifolds T H Colding and W P Minicozzi II
420
Frobenius Manifolds see WDVV Equations and Frobenius Manifolds
425
Mathematical Theory K Schneider and M Farge
426
RiemannHilbert Methods in Integrable Systems D Shepelsky
429
Capillary Surfaces R Finn
431
Minimax Principle in the Calculus of Variations A Abbondandolo
432
RiemannHilbert Problem V P Kostov
436
WDVV Equations and Frobenius Manifolds B Dubrovin
438
A Geometric Survey R P Thomas
439
Riemannian Holonomy Groups and Exceptional
441
Cartan Model see Equivariant Cohomology and the Cartan Model
446
Saddle Point Problems M Schechter
447
Weakly Coupled Oscillators E M Izhikevich and Y Kuramoto
448
rConvergence and Homogenization G Dal Maso
449
Multicomponent Fluids see Interfaces and Multicomponent Fluids
459
Wightman Axioms see Axiomatic Quantum Field Theory
462
Gauge Theories from Strings P Di Vecchia
463
Multiscale Approaches A Lesne
465
Central Manifolds Normal Forms P Bonckaert
467
Scattering Asymptotic Completeness and Bound States D lagolnitzer and J Magnen
475
Experimental Tests C M Will
481
Negative Refraction and Subdiffraction Imaging S OBrien and S A Ramakrishna
483
Schrodinger Operators V Bach
487
Characteristic Classes P B Gilkey R Ivanova and S Nikcevic
488
Newtonian Fluids and Thermohydraulics G Labrosse and G Kasperski
492
Generic Properties of Dynamical Systems C Bonatti
494
Newtonian Limit of General Relativity J Ehlers
503
Noncommutative Geometry and the Standard Model T Schucker
509
Geometric Flows and the Penrose Inequality H Bray
510
Classical rMatrices Lie Bialgebras and Poisson Lie Groups M A SemenovTianShansky
511
Semiclassical Approximation see Stationary Phase Approximation Normal Forms
512
Noncommutative Geometry from Strings ChongSun Chu
515
RELATED MATHEMATICS
517
Semilinear Wave Equations P DAncona
518
Noncommutative Tori YangMills and String Theory A Konechny
524
Separation of Variables for Differential Equations S RauchWojciechowski and K Marciniak
526
Quantization Methods and Path
528
Overview G Gallavotti
530
Cluster Expansion R Kotecky
531
Separatrix Splitting D Treschev
535
Dynamical Systems Approach P Butta and C Marchioro
540
Cohomology Theories U Tillmann
545
GinzburgLandau Equation Y Morita
547
Compact Manifolds A Huckleberry and T Peternell
551
Nonlinear Schrodinger Equations M J Ablowitz and B Prinari
552
Dynamical Evolution S Franz
553
Differential Geometry
559
Graded Poisson Algebras A S Cattaneo D Fiorenza and R Longoni
560
Gravitational Lensing J Wambsganss
567
Nonperturbative and Topological Aspects of Gauge Theory R W Jackiw
568
Shock Waves see Symmetric Hyperbolic Systems and Shock Waves
570
Gravitational VBody Problem Classical D C Heggie
575
Compact Groups and Their Representations A Kirillov and A Kirillov Jr
576
Normal Forms and Semiclassical Approximation D Bambusi
578
Gravitational Waves G Gonzalez and J Pullin
582
Singularities of the Ricci Flow M Anderson
584
WParticle Quantum Scattering D R Yafaev
585
Stochastic Methods
586
Nuclear Magnetic Resonance P T Callaghan
592
Sobolev Spaces see Inequalities in Sobolev Spaces
594
Mathematical Theory GQ Chen
595
212
600
Equilibrium Statistical Mechanics
602
Hamiltonian Reduction of Einsteins Equations A E Fischer and V Moncrief
607
Operads J Stasheff
609
Operator Product Expansion in Quantum Field Theory H Osborn
616
Spacetime Topology Causal Structure and Singularities R Penrose
617
Special Lagrangian Submanifolds see Calibrated Geometry and Special Lagrangian Submanifolds
623
Obstructions to Integrability M Irigoyen
624
Optimal Cloning of Quantum States M Keyl
628
Stability and Instability Theory P Bernard
631
Spectral Theory of Linear Operators M Schechter
633
Variational Techniques
636
Ordinary Special Functions W Van Assche
637
Condensed Matter and Optics
645
Lie Groups and Lie Algebras
646
Holomorphic Dynamics M Lyubich
652
Spin Glasses F Guerra
655
Holonomic Quantum Fields J Palmer
660
Spinors and Spin Coefficients K P Tod
667
Homoclinic Phenomena S E Newhouse
672
Integrable Systems
673
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