Program
17/11 Propagation in imaginary time and Matsubara formalism. Single- and two-particle Green's functions, and relationship with physical obervables.
19/11 Perturbation theory in imaginary time: general formalism and Wick's theorem.
24/11 Perturbative expansion of the single-electron Green's function in powers of the electron-electron interaction. Feynman diagram representation of the perturbation series.
26/11 Dyson equation, self-energy and its physical meaning.
1/12 Perturbative expansion of the two-electron Green's function in powers of the electron-electron interaction. Four-leg vertices and Bethe-Salpeter equations.
3/12 Three-leg vertices and linear response functions in perturbation theory.
8/12 Conservation laws and Ward-Takahashi identities.
10/12 Conserving approximations and few examples.
15/12 Luttinger-Ward functional, free-energy and Luttinger's theorem
17/12 Diagrammatic expansion in other perturbations: electron-phonon/photons/etc.. coupling, external fields, impurity potential.