Many Particle Strongly Interacting Systems.pdf


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arXiv:cond-mat/0208219 v1 12 Aug 2002

Irreducible Green Functions Method and
Many-Particle Interacting Systems on a
Lattice ∗
A.L.Kuzemsky †
Bogoliubov Laboratory of Theoretical Physics,
Joint Institute for Nuclear Research,
141980 Dubna, Moscow Region, Russia.

Abstract
The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of
motion method for double-time temperature dependent Green functions (GFs) is presented. This method was developed to overcome
some ambiguities in terminating the hierarchy of the equations of motion of double-time Green functions and to give a workable technique
to systematic way of decoupling. The approach provides a practical
method for description of the many-body quasi-particle dynamics of
correlated systems on a lattice with complex spectra. Moreover, it
provides a very compact and self-consistent way of taking into account
the damping effects and finite lifetimes of quasi-particles due to inelastic collisions. In addition, it correctly defines the Generalized Mean
Fields (GMF), that determine elastic scattering renormalizations and
, in general, are not functionals of the mean particle densities only. The
purpose of this article is to present the foundations of the IGF method.
The technical details and examples are given as well. Although some
space is devoted to the formal structure of the method, the emphasis
is on its utility. Applications to the lattice fermion models such as
Hubbard/Anderson models and to the Heisenberg ferro- and antiferromagnet, which manifest the operational ability of the method are
given. It is shown that the IGF method provides a powerful tool for
the construction of essentially new dynamical solutions for strongly interacting many-particle systems with complex spectra.




”Rivista del Nuovo Cimento” vol.25, N 1 (2002) pp.1-91
E-mail:kuzemsky@thsun1.jinr.ru; http://thsun1.jinr.ru∼ kuzemsky