Research on electronic systems in condensed matter physics is at present developing very rapidly, where the main focus is changing from the "single-particle problem" to the "many-particle problem". That is, the main research interest changed from phenomena that can be understood in the single particle picture, as, for example, in band theory, to phenomena that arise owing to the interaction between many electrons.

1.The One-Dimensional Quantum Spin Chain

1.1 The S = 1/2 XXZ Spin Chain

1.2 The Jordan-Wigner Transformation and the Quantum Kink

1.3 The Bethe Ansatz and the Exact Solution

2.Quantum Field Theory in 1+1 Dimensions

2.1 Bosonization

2.2 Conformal Field Theory

2.3 The Non-linear Sigma Model

3.Strongly Correlated Electronic Systems

3.1 Models of Strongly Correlated Electronic Systems

3.2 Spin-Charge Separation in One Dimension

3.3 Magnetic Ordering in Strongly Correlated Electronic Systems

3.4 Self-consistent Renormalization Theory

4.Local Electron Correlation

4.1 The Kondo Effect

4.2 Dynamical Mean Field Theory

5.Gauge Theory of Strongly Correlated Electronic Systems

5.1 Gauge Theory of Quantum Anti-ferromagnets

5.2 Gauge Theory of the Doped Mott Insulator

5.3 Gauge Theory of Quantum Hall Liquids

Appendix

A.Complex Functions

A.1  Projection from the z-Plane to the w-Plane

A.2  Contour Integral of f（z） Around the Path C

B.The Variational Principle and the Energy-Momentum Tensor

Literature

Index