Second quantization for fermions and bosons. Two-paricle states and interactions. Mean-field
techniques. Perturbation series for the single-particle propagator. Feynman diagrams. Dyson
equation, two-particle propagator and vertex function. Nonperturbative aspects. Hartree-Fock in
atoms and molecules. Study of second-order selfenergy: static and dynamic contributions.
Quasiparticles in Landau-Migdal framework. Excited states. Collective motion. Random phase
approximation. Plasmon excitations in the electron gas. Repulsive short-range interactions.
Ladder diagrams. Saturation in nuclear matter. Boson systems. Bose-Einstein condensation.
Gross-Pitaevskii equation for ultracold atomic gases. Bogoliubov perturbation theory.
Hugenholtz-Pines theorem. first-order results for dilute Bose gas. Superfluidity in Helium-4.
Pairing in fermion systems. BCS theory and metallic superconductivity. Non-Fermi liquids.
Final competences:
1 Familiarity with a number of basic concepts in quantum many body systems and condensed matter physics.
2 Having an overview about different phases of quantum matter, and the associated phenomenology (gapless edge modes, topological entanglement entropy,…)
3 Ability to read scientific papers about recent developments and to start research in this field.
