凝聚态物理学中的量子场论

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.

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 limitPreface 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