sentences:  This advanced and notable 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, this method 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.