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The concept of electronic correlations plays an important role in moderncondensed matter physics. It refers to interaction effects which cannot beexplained within a static mean-field picture as provided by Hartree-Focktheory. Electronic correlations can have a very strong influence on theproperties of materials. For example, they may turn a metal into an insulator(Mott-Hubbard metal-insulator transition). In these lecture notes I (i)introduce basic notions of the physics of correlated electronic systems, (ii)discuss the construction of mean-field theories by taking the limit of highlattice dimensions, (iii) explain the simplifications of the many-bodyperturbation theory in this limit which provide the basis for the formulationof a comprehensive mean-field theory for correlated fermions, the dynamicalmean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and(vi) apply the DMFT to investigate electronic correlations in models andmaterials.

Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials