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1．Review of Quantum Mechanics and Basic Principles of Field Theory 1

1.1 Single-Particle Quantum Mechanics 1

1.2 Many-Particle Quantum Mechanics:Second Quantization 12

1.3 The Variation Principle and the Noether Theorem 18

1.4 Quantization of the Electromagnetic Field 23

2．Quantization with Path Integral Methods 27

2.1 Single-Particle Quantum Mechanics and Path Integrals 27

2.2 The Path Integral for Bosons 37

2.3 The Path Integral for Fermions 42

2.4 The Path Integral for the Gauge Field 45

2.5 The Path Integral for the Spin System 47

3．Symmetry Breaking and Phase Transition 51

3.1 Spontaneous Symmetry Breaking 51

3.2 The Goldstone Mode 60

3.3 Kosterlitz-Thouless Transition 68

3.4 Lattice Gauge Theory and the Confinement Problem 78

4．Simple Examples for the Application of Field Theory 91

4.1 The RPA Theory of a Coulomb Gas 91

4.2 The Bogoliubov Theory of Superfluidity 102

5．Problems Related to Superconductivity 113

5.1 Superconductivity and Path Integrals 113

5.2 Macroscopic Quantum Effects and Dissipation:The Josephson Junction 133

5.3 The Superconductor-Insulator Phase Transition in Two Dimensions and the Quantum Vortices 146

6．Quantum Hall Liquid and the Chern-Simons Gauge Field 161

6.1 Two-Dimensional Electron System 161

6.2 Effective Theory of a Quantum Hall Liquid 167

6.3 The Derivation of the Laughlin Wave Function 186

Appendix 193

A．Fourier Transformation 193

B．Functionals and the Variation Principle 195

C．Quantum Statistical Mechanics 199

References 201

Index 205