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1 Second Quantisation1£®1 Identical Particles1£®2 The \"Continuous\" Fock Representation1£®3 The \"Discrete\" Fock Representation1£®4 Exercises1£®5 Self-Examination Questions2 Many-Body Model Systems2£®1 Crystal Electrons2£®1£®1 Non-interacting Bloch Electrons2£®1£®2 The Jellium Model2£®1£®3 The Hubbard Model2£®1£®4 Exercises2£®2 Lattice Vibrations2£®2£®1 The Harmonic Approximation2£®2£®2 The Phonon Gas2£®2£®3 Exercises2£®3 The Electron-Phonon Interaction2£®3£®1 The Hamiltonian2£®3£®2 The Effective Electron-Electron Interaction2£®3£®3 Exercises2£®4 Spin Waves2£®4£®1 Classification of Magnetic Solids2£®4£®2 Model Concepts2£®4£®3 Magnons2£®4£®4 The Spin-Wave Approximation2£®4£®5 Exercises2£®5 Self-Examination Questions3 Green's Funetions3£®1 Preliminary Considerations3£®1£®1 Representations3£®1£®2 Linear-Response Theory3£®1£®3 The Magnetic Susceptibility3£®1£®4 The Electrical Conductivity3£®1£®5 The Dielectric Function3£®1£®6 Spectroscopies£¬ Spectral Density3£®1£®7 Exercises3£®2 Double-Time Green's Functions3£®2£®1 Equations of Motion3£®2£®2 Spectral Representations3£®2£®3 The Spectral Theorem3£®2£®4 Exact Expressions3£®2£®5 The Kramers-Kronig Relations3£®2£®6 Exercises3£®3 First Applications3£®3£®1 Non-Interacting Bloch Electrons3£®3£®2 Free Spin Waves3£®3£®3 The Two-Spin Problem3£®3£®4 Exercises3£®4 The Quasi-Particle Concept3£®4£®1 One-Electron Green's Functions3£®4£®2 The Electronic Self-Energy3£®4£®3 Quasi-Particles3£®4£®4 Quasi-Particle Density of States3£®4£®5 Internal Energy3£®4£®6 Exercises3£®5 Self-Examination Questions4 Systems of Interacting Particles4£®1 Electrons in Solids4£®1£®1 The Limiting Case of an Infinitely Narrow Band4£®1£®2 The Hartree-Fock Approximation4£®1£®3 Electronic Correlations4£®1£®4 The Interpolation Method4£®1£®5 The Method of Moments4£®1£®6 The Exactly Half-filled Band4£®1£®7 Exercises4£®2 Collective Electronic Excitations4£®2£®1 Charge Screening £¨Thomas-Fermi Approximation£©4£®2£®2 Charge Density Waves£¬ Plasmons4£®2£®3 Spin Density Waves£¬ Magnons4£®2£®4 Exercises4£®3 Elementary Excitations in Disordered Alloys4£®3£®1 Formulation of the Problem4£®3£®2 The Effective-Medium Method4£®3£®3 The Coherent Potential Approximation4£®3£®4 Diagrammatic Methods4£®3£®5 Applications4£®4 Spin Systems4£®4£®1 The Tyablikow Approximation4£®4£®2 \"Renormalised\" Spin Waves4£®4£®3 Exercises4£®5 The Electron-Magnon Interaction4£®5£®1 Magnetic 4f Systems £¨s-f-Model£©4£®5£®2 The Infinitely Narrow Band4£®5£®3 The Alloy Analogy4£®5£®4 The Magnetic Polaron4£®5£®5 Exercises4£®6 Self-Examination Questions5 Perturbation Theory £¨T = 0£©5£®1 Causal Green's Functions5£®I£®1 \"Conventional\" Time-dependent Perturbation Theory5£®1£®2 \"Switching on\" the Interaction Adiabatically5£®1£®3 Causal Green's Functions5£®1£®4 Exercises5£®2 Wick's Theorem5£®2£®1 The Normal Product5£®2£®2 Wick's Theorem5£®2£®3 Exercises5£®3 Feynman Diagrams5£®3£®1 Perturbation Expansion for the Vacuum Amplitude5£®3£®2 The Linked-Cluster Theorem5£®3£®3 The Principal Theorem of Connected Diagrams5£®3£®4 Exercises5£®4 Single-Particle Green's Functions5£®4£®1 Diagrammatic Perturbation Expansions5£®4£®2 The Dyson Equation5£®4£®3 Exercises5£®5 The Ground-State Energy of the Electron Gas £¨Jellium Model£©5£®5£®1 First-Order Perturbation Theory5£®5£®2 Second-Order Perturbation Theory5£®5£®3 The Correlation Energy5£®6 Diagrammatic Partial Sums5£®6£®1 The Polarisation Propagator5£®6£®2 Effective Interactions5£®6£®3 Vertex Function5£®6£®4 Exercises5£®7 Self-Examination Questions6 Perturbation Theory at Finite Temperatures6£®1 The Matsubara Method6£®1£®1 Matsubara Functions6£®1£®2 The Grand Canonical Partition Function6£®1£®3 The Single-Particle Matsubara Function6£®2 Diagrammatic Perturbation Theory6£®2£®1 Wick's Theorem6£®2£®2 Diagram Analysis of the Grand-Canonical Partition Function6£®2£®3 Ring Diagrams6£®2£®4 The Single-Particle Matsubara Function6£®3 Self-Examination QuestionsSolutions of the ExercisesIndex