The Large N Expansion in Quantum Field Theory and Statistical Physics: From Spin Systems to 2-dimensional Gravity

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World Scientific, 1993 - Science - 1130 pages
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This book contains an edited comprehensive collection of reprints on the subject of the large N limit as applied to a wide spectrum of problems in quantum field theory and statistical mechanics. The topics include (1) Spin Systems; (2) Large N Limit of Gauge Theories; (3) Two-Dimensional QCD; (4) Exact Results on Planar Perturbation Series and the Nature of the 1/N Series; (5) Schwinger-Dyson Equations Approach; (6) QCD Phenomenological Lagrangians and the Large N Limit; (7) Other Approaches to Large N: Eguchi-Kawai Model, Collective Fields and Numerical Methods; (8) Matrix Models; (9) Two-Dimensional Gravity and String Theory.
 

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Contents

Critical Behavior of a Classical Heisenberg Ferromagnet with
7
Introduction to the Renormalization Group
15
A Reduced Model for LargeAT
31
Critical Exponent n up to 1n2 for the ThreeDimensional
41
Spontaneous Breakdown of Continuous Symmetries Near
53
A 1n Expandable Series of NonLinear a Models with
64
Large 2V Limit of Gauge Theories
79
TwoDimensional QCD
93
Matrix Models
565
Possible ThirdOrder Phase Transition in the LargeN Lattice
584
N oo Phase Transition in a Class of Exactly Soluble Model
592
The External Field Problem in the Large N Limit of QCD
600
A Method of Integration over Matrix Variables
616
II
630
TwoDimensional Gravity and String Theory
639
A Simpler Expression for Planar Field Theories 385
642

A Model of Quark
104
Confinement Form Factors and DeepInelastic Scattering
125
PathOrdered Operator Formalism of Gauge Theories
146
Exact Results on Planar Perturbation Series
153
Construction and Borel Summability of Planar Four
182
SchwingerDyson Equations Approach
225
Computation of the Wilson Loop Functional
239
QCD Phenomenological Lagrangians and
247
Baryons in the lN Expansion
254
Current Algebra Baryons and Quark Confinement
309
Collective Coordinates of the Topological
322
LargeTV QCD Baryon Dynamics Exact Results from
335
ChiralSymmetry Breakdown in LargeTV Chromodynamics
348
Anomalies
356
From Quarks to Solitons
368
Reduction of Dynamical Degrees of Freedom in the LargeTV
377
The Quantum Collective Field Method and Its Application
402
SUoo Gauge Theories on Asymmetric Lattices
419
Momentum Loop Dynamics and Random Surfaces in QCD
425
II Implementation
446
Planar Diagrams TwoDimensional Lattice Gravity
645
Bilocal Regularization of Models of Random Surfaces
659
The Appearance of Matter Fields from Quantum Fluctuations
682
The YangLee Edge Singularity on a Dynamical Planar
697
Exactly Solvable Field Theories of Closed Strings
711
Strings in Less Than One Dimension
718
Nonperturbative TwoDimensional Quantum Gravity
738
Strings in Less Than One Dimension and the Generalized
775
Microscopic and Macroscopic Loops in NonPerturbative
780
The Supersymmetric OneDimensional String
788
A NonPerturbative Ambiguity Free Solution of a String Model
794
The Strength of NonPerturbative Effects in String Theory
809
Continuum SchwingerDyson Equations and Universal
820
Loop Equations and Virasoro Constraints in NonPerturbative
842
SchwingerDyson Equations for the TwoMatrix Model
864
TwoDimensional Gravity and Intersection Theory
871
Integrability in Random Matrix Models
939
Spectrum
946
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