Preface 前言 Chapter 1 Overview 概述 1.1 Orientation 研究方向 1.2 An experiment—ballistic expansion 一个实验——弹道展开 1.3 One dimension versus two or three dimensions 一维与二维或三维 1.4 Quantum mechanics 量子力学 1.5 The essence of the Bethe ansatz 贝脱方案的实质 1.6 A simple example—the 1/r2 potential 一个简单的例子——1/r2势 1.7 References and history 参考文献和历史事件 Chapter 2 Integrability and Nondiffraction 可积性和非衍射 2.1 What does it mean to say that a system is integrable 一个系统可积意味着什么 2.2 Scattering without diffraction 无衍射效应的散射 2.3 Proof of integrability for the hyperbolic potential 双曲势可积性的证明 2.4 The δ-function potentia δ函数势 2.5 Adding periodic boundary conditions 添加周期性边界条件 2.6 This is not a low-density approximation 这不是低密度近似 Chapter 3 Techniques 技巧 3.1 Our fundamental equation 基本方程 3.2 The ground state 基态 3.3 Response of the ground state 基态的响应 3.4 Excitations near the ground state 基态附近的激发 3.5 Zero-temperature thermodynamics 零温热力学 3.6 Finite temperature thermodynamics 有限温度热力学 3.7 The inverse-square potential—an example 一个例子——平方反比势 Chapter 4 The Classical Limit 经典极限 4.1 Classical diffraction—pictures from an exhibition 图片展示——经典衍射 4.2 The classical limit 经典极限 4.3 Classical system at zero temperature 零温时的经典系统 4.4 The inverse-square limit—example 1 例1——平方反比极限 4.5 The Toda limit—example 2 例2——户田极限 4.6 Solitons and constant profile solutions 孤子和形状不变解 Chapter 5 Groundstate Wavefunctions of Product Form 乘积形式的基态波函数 5.1 An ansatz for the ground state wavefunction 基态波函数的假设 5.2 Excited states for the trigonometric case 三角问题的激发态 5.3 Ground state correlations for the trigonometric case 三角问题中的基态关联 Chapter 6 The Heisenberg-Ising Model 海森伯-伊辛模型 6.1 The model and its symmetries 模型及其对称性 6.2 Bethe′s ansatz 贝脱方案 6.3 The dilute limit M＜＜N 低密度极限M＜＜N 6.4 A change of variables 变量的改变 6.5 The ground state 基态 6.6 Perturbations and excitations of the ground state 基态的微扰和激发 6.7 Zero-temperature thermodynamics 零温热力学 6.8 The low-density limit and complex solutions 低密度极限和复杂解 6.9 Further results 进一步的结果 Chapter 7 Consistency 一致性 7.1 How can we show integrability 如何证明可积性 7.2 How can we show non-integrability 如何证明不可积性 7.3 Consistency conditions 一致性条件 7.4 Solution to consistency conditions 一致性条件的解 7.5 Periodic and twisted boundary conditions 周期性边界条件和扭曲的边界条件 7.6 Eigenvectors of the transfer matrix，two-components 转移矩阵的本征矢，二分量 7.7 Eigenvectors of the transfer matrix: multicomponent system 转移矩阵的本征矢，多分量系统 7.8 The constructive approach 构造法 Chapter 8 Exchange Models 交换模型 8.1 Hyperbolic exchange models 双曲交换模型 8.2 Integrability 可积性 8.3 The two-body phase shifts 二体相移 8.4 The inverse-square exchange potential 平方反比交换势 8.5 The δ-function potential δ 函数势 Chapter 9 The Sinh-Cosh Model 双曲正弦-双曲余弦模型 9.1 The sinh-cosh potential 双曲正弦-双曲余弦势 9.2 Integrability 可积性 9.3 The two-body problem 二体问题 9.4 Phase shifts 相移 9.5 Spin waves 自旋波 9.6 Solution and results for zero temperature and zero spin/charge 零温和零自旋/电荷的解和结论 Chapter 10 Exchange Lattice Systems by Freezing 冻结的交换晶格系统 10.1 Freezing continuum models to give lattice models 从连续模型的冻结到晶格模型 10.2 Review of the continuum exchange model 连续交换模型的回顾 10.3 The limit λ→∞ λ→∞极限 10.4 The first order equation 一阶方程 10.5 The densities ρ(x) and e(x) 密度ρ(x) 和e(x) 10.6 Results for the nearest-neighbor model 最近邻模型的结果 10.7 Results for the hyperbolic model 双曲模型的结果 10.8 The inverse-square lattice at finite temperature 有限温度的平方反比晶格 Chapter 11 The Hubbard Model 赫伯德模型 11.1 The model and its symmetries 模型及其对称性 11.2 Bethe′s ansatz 贝脱方案 11.3 The repulsive case 排斥情况 11.4 The attractive case 吸引情况 11.5 Excitations at the symmetric point 对称点的激发 Appendix A Some Two-Body Problems 几个二体问题 A.1 The two-body problem 二体问题 A.2 The potential v(r)=cδ(r) v(r)=cδ(r) 势 A.3 The potential v(r)=λ(λ-1)/r2 v(r)=λ(λ-1)/r2势 A.4 The potential v(r)=λ(λ-1)/sin h2r v(r)=λ(λ-1)/sin h2r势 A.5 The potential v(r)=-λ(λ-1)/cos h2r v(r)=-λ(λ-1)/cos h2r势 A.6 Combination potentials 混合势 Appendix B Representations 表象 B.1 The permutation group 置换群 B.2 The twisted permutation group 扭曲的置换群 B.3 Two ways to write the Bethe ansatz 贝脱方案的两种表述 B.4 Two-body scattering 二体散射 B.5 The consistency conditions 一致性条件 B.6 Representations 表象 B.7 Twisted boundary conditions 扭曲的边界条件 B.8 Realizations 实现 Bibliography 文献目录 Index 索引
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