Interacting fermions : Introduction to dynamic mean field theory

Quantum systems made up of a very large number of interacting particles - electrons in a material or quantum fluids such as ultra-cold gases - display fascinating collective phenomena. As early as 1929, Dirac stressed the need to develop theoretical methods to understand the physics of these systems, and even to predict their properties. Today, this research program closely combines conceptual and computational/algorithmic aspects. This year's lecture is devoted to the " dynamic mean field theory ", which has led to significant progress in this field. This approach offers a radically different physical description of a weakly interacting electron gas. An introduction to the basics and the most recent developments will be presented, in particular through seminars and a colloquium - - without forgetting the link with experimental observations.