目錄
1 Second Quantisation
1.1 Identical Particles
1.2 The "Continuous" Fock Representation
1.3 The "Discrete" Fock Representation
1.4 Exercises
1.5 Self-Examination Questions
2 Many-Body Model Systems
2.1 Crystal Electrons
2.1.1 Non-interacting Bloch Electrons
2.1.2 The Jellium Model
2.1.3 The Hubbard Model
2.1.4 Exercises
2.2 Lattice Vibrations
2.2.1 The Harmonic Approximation
2.2.2 The Phonon Gas
2.2.3 Exercises
2.3 The Electron-Phonon Interaction
2.3.1 The Hamiltonian
2.3.2 The Effective Electron-Electron Interaction
2.3.3 Exercises
2.4 Spin Waves
2.4.1 Classification of Magnetic Solids
2.4.2 Model Concepts
2.4.3 Magnons
2.4.4 The Spin-Wave Approximation
2.4.5 Exercises
2.5 Self-Examination Questions
3 Green's Funetions
3.1 Preliminary Considerations
3.1.1 Representations
3.1.2 Linear-Response Theory
3.1.3 The Magnetic Susceptibility
3.1.4 The Electrical Conductivity
3.1.5 The Dielectric Function
3.1.6 Spectroscopies, Spectral Density
3.1.7 Exercises
3.2 Double-Time Green's Functions
3.2.1 Equations of Motion
3.2.2 Spectral Representations
3.2.3 The Spectral Theorem
3.2.4 Exact Expressions
3.2.5 The Kramers-Kronig Relations
3.2.6 Exercises
3.3 First Applications
3.3.1 Non-Interacting Bloch Electrons
3.3.2 Free Spin Waves
3.3.3 The Two-Spin Problem
3.3.4 Exercises
3.4 The Quasi-Particle Concept
3.4.1 One-Electron Green's Functions
3.4.2 The Electronic Self-Energy
3.4.3 Quasi-Particles
3.4.4 Quasi-Particle Density of States
3.4.5 Internal Energy
3.4.6 Exercises
3.5 Self-Examination Questions
4 Systems of Interacting Particles
4.1 Electrons in Solids
4.1.1 The Limiting Case of an Infinitely Narrow Band
4.1.2 The Hartree-Fock Approximation
4.1.3 Electronic Correlations
4.1.4 The Interpolation Method
4.1.5 The Method of Moments
4.1.6 The Exactly Half-filled Band
4.1.7 Exercises
4.2 Collective Electronic Excitations
4.2.1 Charge Screening （Thomas-Fermi Approximation）
4.2.2 Charge Density Waves, Plasmons
4.2.3 Spin Density Waves, Magnons
4.2.4 Exercises
4.3 Elementary Excitations in Disordered Alloys
4.3.1 Formulation of the Problem
4.3.2 The Effective-Medium Method
4.3.3 The Coherent Potential Approximation
4.3.4 Diagrammatic Methods
4.3.5 Applications
4.4 Spin Systems
4.4.1 The Tyablikow Approximation
4.4.2 "Renormalised" Spin Waves
4.4.3 Exercises
4.5 The Electron-Magnon Interaction
4.5.1 Magnetic 4f Systems （s-f-Model）
4.5.2 The Infinitely Narrow Band
4.5.3 The Alloy Analogy
4.5.4 The Magnetic Polaron
4.5.5 Exercises
4.6 Self-Examination Questions
5 Perturbation Theory （T = 0）
5.1 Causal Green's Functions
5.I.1 "Conventional" Time-dependent Perturbation Theory
5.1.2 "Switching on" the Interaction Adiabatically
5.1.3 Causal Green's Functions
5.1.4 Exercises
5.2 Wick's Theorem
5.2.1 The Normal Product
5.2.2 Wick's Theorem
5.2.3 Exercises
5.3 Feynman Diagrams
5.3.1 Perturbation Expansion for the Vacuum Amplitude
5.3.2 The Linked-Cluster Theorem
5.3.3 The Principal Theorem of Connected Diagrams
5.3.4 Exercises
5.4 Single-Particle Green's Functions
5.4.1 Diagrammatic Perturbation Expansions
5.4.2 The Dyson Equation
5.4.3 Exercises
5.5 The Ground-State Energy of the Electron Gas （Jellium Model）
5.5.1 First-Order Perturbation Theory
5.5.2 Second-Order Perturbation Theory
5.5.3 The Correlation Energy
5.6 Diagrammatic Partial Sums
5.6.1 The Polarisation Propagator
5.6.2 Effective Interactions
5.6.3 Vertex Function
5.6.4 Exercises
5.7 Self-Examination Questions
6 Perturbation Theory at Finite Temperatures
6.1 The Matsubara Method
6.1.1 Matsubara Functions
6.1.2 The Grand Canonical Partition Function
6.1.3 The Single-Particle Matsubara Function
6.2 Diagrammatic Perturbation Theory
6.2.1 Wick's Theorem
6.2.2 Diagram Analysis of the Grand-Canonical Partition Function
6.2.3 Ring Diagrams
6.2.4 The Single-Particle Matsubara Function
6.3 Self-Examination Questions
Solutions of the Exercises
Index
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