April 16-18
Chapter 0, Introduction
§1 Historical overview
§2 The mission, the literature


Chapter 1, Preliminaries: bosons, fermions, second quantisation and what it is good for...
§1 Bosons
1.1 Harmonic oscillator
1.2 Creation/annihilation operators
1.3 Coupled oscillators: the linear chain
1.4 From 1D to 3D, vector fields
1.5 Continuum limit
1.6 Connection to classical field theory, Klein-Gordon equation
1.7 Fields and interactions. Applications
April 23-25
§2 Fermions
2.1 Occupation number representation
2.2 Creation/annihilation operators
2.3 Second quantization
April 30- May 1
2.4 Electrons in solids
§3 Interactions
3.1 Electron-electron interaction
3.2 Electron-phonon interaction
3.3 Phonon-phonon interaction

Chapter 2, Green's functions method
§4 Green's functions at zero temperature
4.1 Schrödinger, Heisenberg and interaction representations
May 7-9
4.2 Scattering matrix
4.3 Green's functions
May 14-16
4.4 Wick's theorem
4.5 Feynman diagrams
4.6 Vacuum polarisation graphs
4.7 Dyson's equation
May 21-23
4.8 Feynman diagrams construction rules
4.9 Two-particle Green's function. Vertex parts and self-energies
4.10 Equations of motion method. Multi-particle correlation functions
May 30
June 4-6
§5 Green's functions technique in non-equilibrium
5.1 The time-loop S-matrix. Keldysh diagrammatics
June 11-13
5.2 Dyson's equation in non-equilibrium
§6 Green's functions technique at finite temperatures
6.1 Introduction
6.2 Matsubara Green's function
June 18-20
6.3 Analytic properties of Green's functions and their interrelation
6.4 Linked cluster expansion
June 25-27
6.5 Linear response theory. Kubo formulas

July 2-4
Chapter 3, Applications of the Green's functions method
§7 Fermi liquid theory
7.1 Adiabatic continuity and quasiparticles
7.2 Finite lifetime of quasiparticles
7.3 Fermi liquid theory of screening and plasmons
7.4 Microscopic foundations of Fermi liquid theory
July 9-11
§8 Superconductivity
8.1 Cooper instability. BCS model of superconductivity
8.2 Calculation of the critical temperature
8.3 Mean field approach. Gorkov's equations and physical properties of superconductors
July 16-18
8.4 Josephson effect
§9 1D electron gases and Luttinger liquids
9.1 Fermi liquid breakdown in one dimension
9.2 The spinlesss Tomonaga-Luttinger (TL) model
9.3 Bosonization of the TL Hamiltonian
July 23-25
9.4 Electron operator in the bosonized form
9.5 Single-particle Green's functions in the TL model
9.6 Examples of (quasi)-1D systems
Conclusions