§1 Historical overview

§2 The mission, the literature

§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

§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

§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