Y $^{′}$( λ ) = − 1 β ∑ − → k σ ∑ ω n { λ − $_{λ}$4 24 − $_{λ}$4 8 − $_{λ}$2 2 − $_{λ}$3 6 − ... + } FIG. 4: The simplest skeleton diagrams for functional Y $^{′}$( λ ). Double dashed lines are tunneling functions T λ ( k ). 6 notion of renormalized tunneling Green’s function T in addition to known before. We have defined correlation function Λ, the mass operator Σ for tunneling function and establish the Dyson equation for them. The mass op- erator was found (13) to be equal to correlation function for λ = 1. By using Fig. 4 for Y $^{′}$( λ ) and the definition of Λ$_{λ}$ of Fig. 2 it is easy to establish the property: We have obtained the diagrammatic representation of the correlation function through the skeleton diagrams which contain the many-particle irreducible Green’s func- tions G (0) ir 2 n with all possible values of n − order of per- turbation theory and the renormalized tunneling Green’s functions. Therefore from (31) and (32) we obtain: We have established the relation between renormalized quantities of thermodynamic potential and one-particle Green’s function. This last function has additional de- pendence on auxiliary constant λ and has to be inte- grated over it. From equation (23) and (33) we have and as the consequence we obtain We have proved the possibility to avoid such integra- tion by λ and to introduce the special functional Y ( λ ) constructed from skeleton diagrams. At the final part of the paper we have proved the sta- tionary property of this functional and found its relation to stationary of thermodynamic potential with respect variation of mass operator or full tunneling function. This theorem is the generalization of known Luttinger and Word theorem [15] proved for weakly correlated sys- tems on the case of strongly correlated systems described with the Hubbard model. Because for λ = 0 perturbation is absent and F (0) = F$_{0}$ , Y (0) = 0 we have Now we can put λ = 1 and to obtain with the stationary property We have developed the diagrammatic theory proposed for Hubbard model many years ago and introduced the Two of us (V.A.M. and L.A.D.) would like to thank Professor N.M. Plakida and Dr. S. Cojocaru for a very helpful discussion. Acknowledgments IV. CONCLUSIONS δF δ Σ = 0 . (38) F (1) = Y (1) + F$_{0}$. (37) F ( λ ) = Y ( λ ) + F$_{0}$. (36) F ( λ ) = Y ( λ ) + const. (35) λ dF ( λ ) dλ = λ dY ( λ ) dλ , (34) λ dY ( λ ) dλ = 1 β ∑ − → k $_{σ}$∑ ω n T$_{λ}$ ( k )Σ$_{λ}$( k ) = 1 β T r ( T$_{λ}$ Σ$_{λ}$) . (33) λ ∂Y $^{′}$( λ ) ∂λ |$_{Σ}$$_{λ}$ = 1 β ∑ − → k $_{σ}$∑ ω n T$_{λ}$ ( k ) λ Λ$_{λ}$( k ) exp( iω$_{n}$ 0 $^{+}$) = 1 β T r ( T$_{λ}$ Λ$_{λ}$) . (32)