这是一本介绍量子场论在凝聚态物理学中应用的好书。书中在介绍了量子场论的基本工具和概念后，着重叙述了量子场论在凝聚态物理学中应用。本书阐述简明、清晰，配有许多生动幽默的插图。内容分4部分，共25章。第一部分介绍了量子场论中的一些重要方法，如：路径积分、费曼图技术和重正化等。第2部分介绍了传统方法在金属电动力学、量子电动力学和A－B效应中的应用。第3部分和第4部分是非微扰技术的应用，主要处理涨落自旋系统，共形对称性，kondo链以及其它相关问题。

Preface to the first edition

Preface to the second edition

Acknowledgements for the first edition

Acknowledgements for the second edition

Ⅰ Introduction to methods

 1 QFT:language and goals

 2 Connection between quantum and classical: path integrals

 3 Definitions of correlation functions: Wick's theorem

 4 Free bosonie field in an external field

 5 Perturbation theory: Feynman diagrams

 6 Calculation methods for diagram series: divergences and their elimination

 7 Renormalization group procedures

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

 9 Nonlinear sigma models in two dimensions: renormalization group and1/N-expansion

 10 0(3) nonlinear sigma model in the strong coupling limit

Ⅱ Fermions

 11 Path integral and Wick's theorem for fermions

 12 Interacting electrons: the Fermi liquid

 13 Electrodynamics in metals

 14 Relativistic fermions: aspects of quantum electrodynamics

(1+1)-Dimensional quantum electrodynamics (Schwinger model)

 15 Aharonov-Bohm effect and transmutation of statistics

The index theorem

Quantum Hall ferromagnet

Ⅲ Strongly fluctuatlng spin systems

 Introduction

 16 Schwinger-Wigner quantization procedure: nonlinear sigma models

Continuous field theory for a ferromagnet

Continuous field theory for an antiferromagnet

 17 0(3) nonlinear sigma model in (2 + 1) dimensions: the phase diagram

Topological excitations: skyrmions

 18 Order from disorder

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

 20 Majorana representation for spin S = 1/2 magnets: relationship to Z2

lattice gauge theories

 21 Path integral representations for a doped antiferromagnet

Ⅳ Physics in the world of one spatial dimension

 Introduction

 22 Model of the free bosonic massless scalar field

 23 Relevant and irrelevant fields

 24 Kosteditz-Thouless transition

 25 Conformal symmetry

Gaussian model in the Hamiltonian formulation

 26 Viras'oro algebra

Ward identities

Subalgebra sl(2)

 27 Differential equations for the correlation functions

Coulomb gas construction for the minimal models

 28 Ising model

Ising model as a minimal model

Quantum Ising model

Order and disorder operators

Correlation functions outside the critical point

Deformations of the Ising model

 29 One-dimensional spinless fermions: Tomonaga-Luuinger liquid

Single-electron correlator in the presence of Coulomb interaction

Spin S = 1/2 Heisenberg chain

Explicit expression for the dynamical magnetic susceptibility

 30 One-dimensional fermions with spin: spin-charge separation

Bosonic form of the SUx (2) Kac-Moody algebra

Spin S = 1/2 Tomonaga-Luttinger liquid

Incommensurate charge density wave

Half-filled band

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

Knizhnik-Zamolodchikov (KZ) equations

Conformal embedding

SU1(2) WZNW model and spin S = 1/2 Heisenberg antiferromagnet

SU2(2) WZNW model and the Ising model

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

 33 Semiclassical approach to Wess-Zumino-Novikov-Witten models

 34 Integrable models: dynamical mass generation

General properties of integrable models

Correlation functions: the sine-Gordon model

Perturbations of spin S = 1/2 Heisenberg chain: confinement

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

Single-electron Green's function in a one-dimensional charge density wave state

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

Spin ladder

Correlation functions

Spin S = 1 antiferromagnets

 37 Kondo chain

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

chromodynamics

Select bibliography

Index