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A review of electronic dynamics of single-impurity and many-impurity Andersonmodels is contained in this report. Those models are used widely for many ofthe applications in diverse fields of interest, such as surface physics, theoryof chemisorption and adsorbate reactions on metal surfaces, physics ofintermediate valence systems, theory of heavy fermions, physics of quantum dotsand other nanostructures. While standard treatments are generally based onperturbation methods, our approach is based on the non-perturbative techniquefor the thermodynamic Green functions. The method of the irreducible Greenfunctions is used as the basic tool. This irreducible Green functions methodallows one to describe the quasiparticle spectra with damping of the stronglycorrelated electron systems in a very general and natural way and to constructthe relevant dynamical solution in a self-consistent way on the level of Dysonequation without decoupling the chain of the equations of motion for the Greenfunctions. The subject matter includes the improved interpolating solution ofthe Anderson model. It was shown that an interpolating approximation, whichsimultaneously reproduces the weak-coupling limit up to second order in theinteraction strength U and the strong-coupling limit up to second order in thehybridization V (and thus also fulfils the atomic limit) can be formulatedself-consistently. This approach offers a new way for the systematicconstruction of approximate interpolation dynamical solutions of stronglycorrelated electron systems.

Electronic Dynamics of the Anderson Model. The Many-Body Approach