Quantum Many Body Systems and Strongly Correlated Electrons II

Basic course given by Michele Fabrizio

Term: 2

Start: 17-11-2020 End: 17-12-2020 Room: Online

Credits: 3

Schedule: Tue 14:00 - 16:00, Thu 9:00 - 11:00

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. 
 10/12 Conservation laws and Ward-takahashi indetities.
 15/12 Conserving approximations and few examples.  
 17/12 Diagrammatic expansion in other perturbations: electron-phonon/photons/etc.. coupling, external fields, impurity potential.