Faculty of Science

Objectives

To introduce the modern theories and approaches to many-body effects in strongly correlated electronic systems.

Contents

Elementary excitations in condensed matter; Wave functions of non-interacting bosons and fermions; Occupation number representation and second quantization; Electron gas in a solid: Hartree-Fock approach. Successes and limitations of independent-electron approximations; Linear response theory: static and dynamical screening; Collective excitations (e.g. plamons) by the equation of motion method; Weakly interacting Bose gas; Ground state and broken symmetry; Above-condensate excitations (Bogoliubov transformation); Quantization of lattice vibrations; Consequences of electron-phonon interaction; BCS model, Mean-Field theory, energy gap and single particle excitations; Tight-binding model with electron-electron interactions (Hubbard model); Quantum magnetism: spin waves and broken symmetry; Correlation functions and experiments: the need for a reduced description of many-particle systems; The transition amplitude (Green function) in a system of non interacting particles; Generalization to interacting systems; Analytical properties of the one-particle Green function, quasi particles, transition amplitudes in the presence of interactions, Feynman diagrams, Dyson equations and self-energy.