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Softcover ISBN:  9781470456184 
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Softcover ISBN:  9781470456184 
Product Code:  CLN/32 
List Price:  $55.00 
MAA Member Price:  $49.05 
AMS Member Price:  $40.88 
eBook ISBN:  9781470477936 
Product Code:  CLN/32.E 
List Price:  $55.00 
MAA Member Price:  $49.05 
AMS Member Price:  $40.88 
Softcover ISBN:  9781470456184 
eBook ISBN:  9781470477936 
Product Code:  CLN/32.B 
List Price:  $110.00 $82.50 
MAA Member Price:  $98.10 $73.58 
AMS Member Price:  $81.76 $61.32 

Book DetailsCourant Lecture NotesVolume: 32; 2024; Estimated: 205 ppMSC: Primary 60; 81; 82
This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a wellposed road from simple lattice models to CFTs.
Structured in two parts, the book begins by exploring several twodimensional lattice models, their phase transitions, and their conjectural connection with CFT. Through these lattice models and their local fields, the fundamental ideas and results of twodimensional CFTs emerge, with a special emphasis on the Unitary Minimal Models of CFT. Delving into the delicate ideas that lead to the classification of these CFTs, the authors discuss the assumptions on the lattice models whose scaling limits are described by CFTs. This produces a probabilistic rather than an axiomatic or algebraic definition of CFTs.
Suitable for graduate students and researchers in mathematics and physics, Lattice Models and Conformal Field Theory introduces the ideas at the core of Statistical Field Theory. Assuming only undergraduate probability and complex analysis, the authors carefully motivate every argument and assumption made. Concrete examples and exercises allow readers to check their progress throughout.
Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
ReadershipResearchers interested in probability, mathematical physics, statistical mechanics, and highenergy physics.

Table of Contents

Introduction

Lattice models, phase transitions, and critical exponents

Statistical and quantum field theories

Conformal field theory

Conformal field theory: Minimal models on the plane

Local fields and correlations

Stressenergy tensor and conformal Ward identities

Unitarity and radial quantization

Primary fields and conformal families

Unitary minimal models, lattice models, and loop models

Bibliography

Index


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This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a wellposed road from simple lattice models to CFTs.
Structured in two parts, the book begins by exploring several twodimensional lattice models, their phase transitions, and their conjectural connection with CFT. Through these lattice models and their local fields, the fundamental ideas and results of twodimensional CFTs emerge, with a special emphasis on the Unitary Minimal Models of CFT. Delving into the delicate ideas that lead to the classification of these CFTs, the authors discuss the assumptions on the lattice models whose scaling limits are described by CFTs. This produces a probabilistic rather than an axiomatic or algebraic definition of CFTs.
Suitable for graduate students and researchers in mathematics and physics, Lattice Models and Conformal Field Theory introduces the ideas at the core of Statistical Field Theory. Assuming only undergraduate probability and complex analysis, the authors carefully motivate every argument and assumption made. Concrete examples and exercises allow readers to check their progress throughout.
Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Researchers interested in probability, mathematical physics, statistical mechanics, and highenergy physics.

Introduction

Lattice models, phase transitions, and critical exponents

Statistical and quantum field theories

Conformal field theory

Conformal field theory: Minimal models on the plane

Local fields and correlations

Stressenergy tensor and conformal Ward identities

Unitarity and radial quantization

Primary fields and conformal families

Unitary minimal models, lattice models, and loop models

Bibliography

Index