Many Particle Strongly Interacting Systems.pdf

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ples of the condensed matter theory and statistical mechanics, the physical
properties of this class of materials.
In previous papers, we set up the practical technique of the method of the
irreducible Green functions (IGF) [23] -[33]. This IGF method allows one
to describe quasi-particle spectra with damping for systems with complex
spectra and strong correlation in a very general and natural way. This
scheme differs from the traditional methods of decoupling or terminating
an infinite chain of the equations and permits one to construct the relevant
dynamic solutions in a self-consistent way on the level of the Dyson equation
without decoupling the chain of the equations of motion for the double-time
temperature Green functions. The essence of our consideration of dynamic
properties of many-body system with strong interaction is related closely
with the field theoretical approach, and we use the advantage of the Greenfunction language and the Dyson equation. It is possible to say that our
method emphasizes the fundamental and central role of the Dyson equation
for the single-particle dynamics of many-body systems at finite temperature. This approach has been suggested as essential for various many-body
systems, and we believe that it bears the real physics of interacting manyparticle interacting systems [24], [25].
It is the purpose of the present paper to introduce the concepts of irreducible Green functions (or irreducible operators) and Generalized Mean
Fields (GMF ) in a simple and coherent fashion to assess the validity of
quasi-particle description and mean field theory. The irreducible Green function method is a reformulation of the equation-of-motion approach for the
double-time thermal GFs, aimed of operating with the correct functional
structure of the required solutions. In this sense, it has all advantages and
shortcomings of the Green-function method in comparison, say, with the
functional integration technique, that, in turn, has also its own advantages
and shortcomings. The usefulness of one or another method depends on the
problem we are trying to solve. For the calculation of quasi-particle spectra, the Green-function method is the best. The irreducible-Green-function
method adds to this statement: ”for the calculation of the quasi-particle
spectra with damping” and gives a workable recipe how to do this in a selfconsistent way.
The distinction between elastic and inelastic scattering effects is a fundamental one in the physics of many-body systems, and it is also reflected
in a number of other ways than in the mean-field and finite lifetimes. The
present review attempts to offer a balanced view of quasi-particle interaction
effects in terms of division into elastic- and inelastic-scattering characteristics. For this aim, in the present paper, we discuss the background of the
IGF approach more thoroughly. To demonstrate the general analysis, we
consider here the calculation of quasi-particle spectra and their damping
within various types of correlated electron models to extend the applicability of the general formalism and show flexibility and practical usage of the