Statistical Field Theory An Introduction to Exactly Solved Models in Statistical Physics

by Mussardo, Giuseppe

• ISBN13: 9780199547586
• ISBN10: 0199547580
• Format: Hardcover
• Copyright: 2009-11-02
• Publisher: Oxford University Press

Summary

This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetrybreaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-containedbook provides an excellent introduction to frontier topics of exactly solved models in statistical mechanics and quantum field theory, renormalization group, conformal models, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz and form factor theory. The cleardiscussion of physical principles is accompanied by a detailed analysis of several branches of mathematics, distinguished for their elegance and beauty, such as infinite dimensional algebras, conformal mappings, integral equations or modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail, paying attention to an overall coherent understanding of physical phenomena. Mathematical background isprovided in supplements at the end of each chapter, when appropriate. The chapters are also followed by problems of different levels of difficulty. Advanced undergraduate and graduate students will find a rich and challenging source for improving their skills and for accomplishing a comprehensivelearning of the many facets of the subject.

Author Biography

Giuseppe Mussardo has been Professor of Theoretical Physics at the International School for Advanced Studies (ISAS) in Trieste since 2000, and was Deputy Director of ISAS 2001-2004. He is Head of the Statistical Physics group at ISAS and Coodinator of the European Science Foundation grant INSTANS. He edits Nuclear Physics B: Statistical Mechanics and Field Theory, and JSTAT.

Table of Contents

Introductory Notions

Introduction

One-dimensional systems

Approximate solutions

Bidimensional lattice models

Duality of two-dimensional Ising model

Combinatorial solutions of the Ising model

Transfer matrix of the two-dimensional Ising model

Quantum field theory and conformal variance

Quantum field theory

Renormalization group

Fermionic formulation of the Ising model

Conformal field theory

Minimal conformal models

Conformal field theory of free Bosonic and Fermionic fields

Conformal field theories with extended symmetries

The arena of conformal models

Away from criticality

In the vicinity of the critical points

Integrable quantum field theories

S-matrix theory

Exact S-matrices

Thermodynamics Bethe Ansatz

Form factors and correlation functions

Non-integrable aspects

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