EXACT FUNCTIONALS, EFFECTIVE ACTIONS AND (DYNAMICAL) MEAN-FIELD THEORIES: SOME REMARKS

摘要

In these lecture notes, I would like to discuss (hopefully in a pedagogical manner), a general approach to strongly interacting systems which is based on the construction of a functional of some local quantity (effective action) by the Legendre transform method. This method has a wide range of applicability, ranging from field theory, the statistical mechanics of a classical magnet to interacting fermion systems. Though exact in principle, it requires in practice that the exact functional is approximated in some manner. The examples considered in this lecture will be: the Weiss mean-field theory (MFT) of a classical magnet, the density functional theory (DFT) of the inhomo-geneous electron gas in solids and the dynamical mean-field theory (DMFT) of strongly correlated electron systems.