玻色化已经成为研究现代多体问题的一个非常重要的方法。本书详细说明了玻色化技术及其在强关联系统中的应用。本书内容分为四个部分。第一部分全面介绍玻色化技术，内容包括一维费米子，高斯模型，共形场论中Hilbert空间的结构，两维玻色－爱因斯坦凝聚，非阿贝尔玻色化，Ising模型和WZNW模型。第二部分介绍了玻色化技术在实际模型中的应用，包括Tomonaga－Luttinger液体，一维自旋液体和交换作用交替分布的自旋1/2 Heisenberg模型。第三部分着重介绍了量子杂质问题，内容包括势散射，透射边缘问题，Tomonaga－Luttinger液体中的杂质和多通道近藤问题。

Preface

Acknowledgements

Part Ⅰ: Technical aspects of bosonization

1 A simple case of Bose-Fermi equivalence: Jordan-Wigner transformation

2 One-dimensional fermions. States near the Fermi points

 Ⅰ Chiral anomaly

 Ⅱ Anomalous commutators

3 Ganssian model. Lagrangian formulation

 Ⅰ Bosonization

 Ⅱ Interaction with an electromagnetic field; gauge invariance

4 Conformal symmetry and finite size effects

 Ⅰ Gaussian model in the Hamiltonian formulation

5 Virasoro algebra

 Ⅰ Ward identities

 Ⅱ Subalgebra sl(2)

6 Structure of Hilbert space in conformal theories

 Ⅰ Differential equations for correlation functions

 Ⅱ Dotsenko-Fateev bosonization scheme for the minimal models

7 Current (Kac-Moody) algebras; the first assault

 Ⅰ Sugawara Hamiltonian for Wess-Zumino-Novikov-Witten model

 Ⅱ Knizhnik-Zamolodchikov (KZ) equations

8 Relevant and irrelevant fields

9 Bose-Einstein Condensation in two dimensions; BeresinskiiKosterlJtz-Tbouless transition

10 The sine-Gordon model

 Ⅰ The renormalization group analysis

 Ⅱ Exact solution of the sine-Gordon model

11 Spin S - 1/2 Heiseuherg-lsiug chain

 Ⅰ Explicit expression for the dynamical magnetic susceptibility

12 Isiug model

13 More about the WZNW model

 Ⅰ Special cases

 Ⅰ.1 SU1(2) WZNW model as a Gaussian model

 Ⅰ.2 SU2(2) WZNW model and the Ising model

 Ⅰ.3 SU4(2) as a theory of two bosonic fields

 Ⅰ.4 SU10(2) as a theory of three bosonic fields

 Ⅱ Deformation of the WZNW model and coset constructions

14 Non-Ahelian bosonization

 Ⅰ WZNW model in the Lagrangian formulation

 Ⅱ Derivation of the Lagrangian

 Ⅲ Calculation of a nontrivial determinant

Part Ⅱ: Application of the hesonizatiou technique to physical models in (1+1)-dimemions

15 Interacting fermions with spin

16 Spin-l/2 Tomonaga-Luttinger liquid

17 Instabilities of a Tomouaga-Luttinger liquid

 Ⅰ Electron-phonon interaction

 Ⅰ.1 Incommensurate band filling, the effect on Kc

 Ⅰ.2 Commensurate band filling

 Ⅰ.3 Appendix

 Ⅱ Spectral gap in the spin sector

 Ⅲ Optical conductivity

 Ⅳ Gap in the charge sector at half-filling and the case of small doping

 Ⅴ Appendix. RG equations for the model of one-dimensional electrons from the SU(2) current algebra

18 Interacting fermions with broken spin rotational symmetry

 Ⅰ U(l)-symmetric Thirring model: relation to sine-Gordon and massive Thirfing models

 Ⅱ XYZ Thirring model

 Ⅲ Spin correlation functions

 Ⅳ The role of magnetic field

 Ⅳ.1 Spin-flop transition in the XY'Z model

 Ⅳ.2 Toy model for an orbital antiferromagnet

19 What may happen with a Tomomlln-Lattinger liquid in three dimensions

 Ⅰ Appendix. Fermionic Green's function

 Ⅰ.1 Coordinate space Green's function

 Ⅰ.2 The spectral function (Vc > vs)

 Ⅰ.3 Fourier transform of the Green's function (vc > v,)

 Ⅰ.4 The spectral function, v, > vc

 Ⅰ.5 Fourier transform of Green's function, v, > ve

20 Two weakly coupled Tomonaga--Lm/iager liquids; spinless ease

21 Spin liquids in one dintension: example of spin ladders

 Ⅰ Coupling of identical chains; the Abel/an bosonization

 Ⅱ Correlation functions for the identical chains

 Ⅱ.1 Staggered susceptibility of the conventional (Haldane) spin liquid

 Ⅱ.2 Dimerized spin liquid

 Ⅲ Inequivalent chains; non-Abelian bosonization

 Ⅳ String order parameter in the spin-ladder model

 Ⅴ Appendix A. The topological term emerging from the Wess-Zumino term

 Ⅵ Appendix B. Hidden Z2 ~ Z2 symmetry and string order parameter in the bond-alternating S = 1/2 Heisenberg chain

22 Spin-l/2 Heisenberg chain with alternating exchange

 Ⅰ Appendix. Multiparticle formfactors

23 Superconductivity in a doped spin liquid

 Ⅰ Bosonization and fermionization

 Ⅱ Superconducting fluctuations

 Ⅲ Conclusions

 Ⅳ Appendix. Conditions for suppression of the singie-particle tunneling

24 Edge states in the quantum Hall effect

Part Ⅲ: Single impurity problems

25 Potential scattering

 Ⅰ Introduction

 Ⅱ Reduction of the local scattering problem to one dimension

 Ⅲ The scattering phase

26 X-ray edge problem (Fermi liquids)

 Ⅰ Introduction

 Ⅱ Statement of the problem

 Ⅱ.1 Many-body formulation

 Ⅱ.2 One-particle formulation

 Ⅲ Linked clusters expansion

 Ⅳ Nozieres-De Dominicis solution

 Ⅴ Exact solution for the overlap integral.

 Ⅵ Bosonization approach to the X-ray edge problem

 Ⅵ.1 Boundary condition changing operator (chiral anomaly)

 Ⅵ.2 X-ray response functions via bosonization

 Ⅶ Appendix A. Parquet approximation

 Ⅷ Appendix B. The Wiener-Hopf method

 Ⅸ Appendix C. Orthogonality of Slater determinants

27 Impurities in a Tomonaga-Luttinger liquid

 Ⅰ Introduction

 Ⅱ Weak-coupling analysis of a single impurity

 Ⅱ.1 Bosonization of the impurity Hamiltonian

 Ⅱ.2 Lagrangian formulation: local action

 Ⅱ.3 Renormalization group analysis of local operators

 Ⅲ Strong-coupling analysis

 Ⅲ.1 Open boundary bosonization

 Ⅲ.2 Strong-coupling fixed point

 Ⅳ Exact solution at K = 1/2 and the conductance

 Ⅴ Relation of the impurity backscattering model to the CaldeiraLeggett model

 Ⅵ X-ray edge problem in Tomonaga-Luttinger liquids

28 Multi-channel Kondo problem

 Ⅰ Introduction

 Ⅱ Qualitative analysis

 Ⅲ The Toulouse limit

 Ⅳ The Emery-Kivelson solution

 Ⅳ.1 Green's functions and zero-field free energy

 Ⅳ.2 Magnetic field effects

 Ⅳ.3 Wilson ratio

 Ⅴ The Toulouse limit for the four-channel Kondo model

 Ⅵ Coulomb blockade

 Ⅵ.1 One-dimensional electrons in point contacts

 Ⅵ.2 Coulomb blockade and two-channel Kondo model

General bibliography

Index