## The Large N Expansion in Quantum Field Theory and Statistical Physics: From Spin Systems to 2-dimensional GravityThis 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

### Other editions - View all

### Common terms and phrases

1/N expansion amplitudes antiquark approximation asymptotic asymptotic freedom baryon behavior bilinears Borel bound Brezin calculations chiral coefficients coherent color compute consider contribution convergence corresponding coupling constant critical exponents current algebra cutoff defined derived dimensional dimensions discussion divergent eigenvalues equation euclidean evaluate expectation values fermion Feynman field theory finite form factor formulation free energy gauge invariant gauge theory given glueball gluon graphs Green functions hadronic hamiltonian Hartree Hooft infrared integral interaction Lagrangian large N limit large-TV lattice lattice gauge theories Lett matrix elements meson momenta momentum Nucl observables obtain operators parameters particle perturbation theory Phys physical planar diagrams preprint propagator renormalization group representation result Sakita scalar singularities soliton solution space spin string strong coupling subgraphs symmetry T.A. Dickens theorem tion topological transformation two-dimensional vanish variables Variational algorithm vector vertex vertices Wadia wave function Wilson loop Witten zero