A new approach to the theory of strongly correlated systems

A new diagrammatic method for the investigation of the properties of strongly correlated electron systems is formulated. The method is used in order to handle the strong Coulomb on-site repulsion of the electrons of unfilled inner ion shells of transition and rare earth metals. The new elements of this diagram technique are the many-particle on-site irreducible Green's functions, which contain all the essential spin and charge fluctuations of this system. The infinite sum of such contributions essentially determine the correlation function Z(x, x') which is used to formulate the Dyson equation for renormalized one-particle Green's function. The summing of a class of diagrams permits one to close the equations which determine Z(x, x') function and to discuss Mott-Hubbard and superconducting phase transitions of the system. The influence of strong electron-phonon interaction on the phase transitions is discussed