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內容簡介

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.

內頁插圖

目錄

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

精彩書摘

The related problem is a long-standing problem of the Kondo lattice or, in more generalwords, the problem of the coexistence of conduction electrons and local magnetic moments.We have discussed this problem very briefly in Chapter 21, where it was mentioned that thisremains one of the biggest unsolved problems in condensed matter physics. The only part ofit which is well understood concerns a situation where localized electrons are representedby a single local magnetic moment （the Kondo problem）. In this case we know that thelocal moment is screened at low temperatures by conduction electrons and the ground stateis a singlet. The formation of this singlet state is a nonperturbative process which affectselectrons very far from the impurity. The relevant energy scale （the Kondo temperature） isexponentially small in the exchange coupling constant. It still remains unclear how conduc-tion and localized electrons reconcile with each other when the local moments are arrangedregularly （Kondo lattice problem）. Empirically, Kondo lattices resemble metals with verysmall Fermi energies of the order of several degrees. It is widely believed that conductionand localized electrons in Kondo lattices hybridize at low temperatures to create a singlenarrow band （see the discussion in Chapter 21）. However, our understanding of the detailsof this process remains vague. The most interesting problem is how the localized electronscontribute to the volume of the Fermi sea （according to the large-N approximation, they docontribute）. The most dramatic effect of this contribution is expected to occur in systemswith one conduction electron and one spin per unit cell. Such systems must be insulators（the so-called Kondo insulator）.The available experimental data apparently support thispoint of view: all compounds with an odd number of conduction electrons per spin areinsulators （Aeppli and Fisk, 1992）. At low temperatures they behave as semiconductorswith very small gaps of the order of several degrees. The marked exception is FeSi wherethe size of the gap is estimated as——,700 K （Schlesinger et al., 1993）.

前言/序言

　　The objective of this book is to familiarize the reader with the recent achievements ofquantum field theory （henceforth abbreviated as QFT）. The book is oriented primarilytowards condensed matter physicists but， I hope， can be of some interest to physicists inother fields. In the last fifteen years QFT has advanced greatly and changed its languageand style. Alas， the fruits of this rapid progress are still unavailable to the vast democraticmajority of graduate students， postdoctoral fellows， and even those senior researchers whohave not participated directly in this change. This cultural gap is a great obstacle to thecommunication of ideas in the condensed matter community. The only way to reduce thisis to have as many books covering these new achievements as possible. A few good booksalready exist; these are cited in the select bibliography at the end of the book. Havingstudied them I found， however， that there was still room for my humble contribution. Inthe process of writing I have tried to keep things as simple as possible; the amount offormalism is reduced to a minimum. Again， in order to make life easier for the newcomer， Ibegin the discussion with such traditional subjects as path integrals and Feynman diagrams.It is assumed， however， that the reader is already familiar with these subjects and thecorresponding chapters are intended to refresh the memory. I would recommend those whoare just starting their research in this area to read the first chapters in parallel with someintroductory course in QFT. There are plenty of such courses， including the evergreen bookby Abrikosov， Gorkov and Dzyaloshinsky. I was trained with this book and thoroughlyrecommend it.
　　Why study quantum field theory？ For a condensed matter theorist as， I believe， for otherphysicists， there are several reasons for studying this discipline. The first is that QFT providessome wonderful and powerful tools for our research， The results 凝聚態物理學中的量子場論（第2版） [Quantum Field Theory in Condensed Matter Physics(Second Edition)] 下載 mobi epub pdf txt 電子書

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