Quantum Field Theory in Condensed Matter Physics

by Alexei M. Tsvelik

• ISBN13: 9780521529808
• ISBN10: 0521529808
• Edition: 2nd
• Format: Paperback
• Copyright: 2007-01-18
• Publisher: Cambridge University Press

Summary

This book is a course in modern quantum field theory as seen through the eyes of a theorist working in condensed matter physics. It contains a gentle introduction to the subject and therefore can be used even by graduate students. The introductory parts include a derivation of the path integral representation, Feynman diagrams and elements of the theory of metals including a discussion of Landau'Fermi liquid theory. In later chapters the discussion gradually turns to more advanced methods used in the theory of strongly correlated systems. The book contains a thorough exposition of such non-perturbative techniques as 1/N-expansion, bosonization (Abelian and non-Abelian), conformal field theory and theory of integrable systems. The book is intended for graduate students, postdoctoral associates and independent researchers working in condensed matter physics.

Table of Contents

Preface

Acknowledgements

Introduction to Methods

QFT: language and goals

Connection between quantum and classical: path integrals

Definitions of correlation functions: Wick's theorem

Free bosonic field in an external field

Perturbation theory: Feynman diagrams

Calculation methods for diagram series: divergences and their elimination

Renormalization group procedures

O(N)-symmetric vector model below the transition point

Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion

O(3) nonlinear sigma model in the strong coupling limit

Fermions

Path integral and Wick's theorem for fermions

Interaction electrons: the Fermi liquid

Electrodynamics in metals

Relativistic fermions: aspects of quantum electrodynamics

Aharonov-Bohm effect and transmutation of statistics

Strongly Fluctuating Spin Systems: Introduction

Schwinger-Wigner quantization procedure: nonlinear sigma models

O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram

Order from disorder

Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3

Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories

Path integral representations for a doped antiferromagnet

Physics in the World of One Spatial Dimension: Introduction

Model of the free bosonic massless scalar field

Relevant and irrelevant fields

Kosterlitz-Thouless transition

Conformal symmetry

Virasoro algebra

Differential equations for the correlation functions

Ising model

One-dimensional spinless fermions: Tomonaga-Luttinger liquid

One-dimensional fermions with spin: spin-charge separation

Kac-Moody algebras: Wess-Zumino-Novikov-Witten model

Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization

Semiclassical approach to Wess-Zumino-Novikov-Witten models

Integrable models: dynamical mass generation

A comparative study of dynamical mass generation in one and three dimensions

One-dimensional spin liquids: spin ladder and spin S=1 Heisenberg chain

Kondo chain

Gauge fixing in non-Abelian theories: (1+1)-dimensional quantum chromodynamics

Select bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.