Quantum Many Body Systems and Strongly Correlated Electrons II

1. Propagation in imaginary time and Matsubara formalism. Single- and two-particle Green's functions, and relationship with physical obervables.
2. Perturbation theory in imaginary time: general formalism and Wick's theorem.
3. Perturbative expansion of the single-particle Green's function in powers of the electron-electron interaction. Feynman diagram representation of the perturbation series.    
4. Dyson equation and skeleton diagrams.
5. Self-energy and its physical meaning.
6. Skeleton diagram representation  of the two-particle Green's function. Four-leg vertices and Bethe-Salpeter equations.
7. Three-leg vertices and skeleton diagram representation of linear response functions.
8. Conservation laws and Ward-Takahashi identities.
9. Conserving approximation schemes and selected examples.  
10. Luttinger-Ward functional, free-energy and Luttinger's theorem.

Lecture notes will be provided to the students.