凝聚态物理学中的量子场论 : 第2版

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： Wicks theorem

4 Free bosonic 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 and 1/N-expansion

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

Ⅱ Fermions

11 Path integral and Wicks 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 fluctuagng spin systems

Introduction

16 Schwinger-Wigner quantization procedure： nonlinear sigma models

Continuous field theory for a ferromagnet

Continuous field theory for an antiferromagnet

17 O(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

N Physics in the world of one spatial dimension

Introduction

22 Model of the free bosonic massless scalar field

23 Relevant and irrelevant fields

24 Kosterlitz-Thouless transition

25 Conformal symmetry

Gaussian model in the Hamiltonian formulation

26 Virasoro 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 lsing model

Order and disorder operators Correlation functions outside the critical point Deformations of the Ising model

29 One-dimensional spinless fermions： Tomonaga-Luttinger 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 SU1 (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

SUI(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 Greens 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

This book is a course in modern quantum field theory as seen through the eyes of a theoristworking in condensed matter physics. It contains a gentle introduction to the subject andcan therefore be used even by graduate students. The introductory parts include a deriva-tion of the path integral representation, Feynman diagrams and elements of the theory ofmetals including a discussion of Landau Fermi liquid theory. In later chapters the discus-sion gradually turns to more advanced methods used in the theory of strongly correlatedsystems. The book contains a thorough exposition of such nonperturbative techniques as1/N-expansion, bosonization （Abelian and non-Abelian）, conformal field theory and theoryof integrable systems. The book is intended for graduate students, postdoctoral associatesand independent researchers working in condensed matter physics.