G c Λ V acuum diagram λ 2 − λ 8 2 − λ 6 4 − λ 6 8 − λ 4 8 9 FIG. 9: Three possibilities to obtain one of the vacuum diagram of eight order of perturbation theory. βY ′ = 3 4 V 2 2 1 2 1 2 5 6 − − V 4 8 1 2 3 4 − V 6 48 − V 8 384 1 2 3 4 5 6 7 8 $^{+}$... 1 2 3 4 5 6 7 8 − V 8 48 a ) b ) c ) d ) e ) FIG. 10: Skeleton diagrams for functional Y $^{′}$. × G c α$_{5}$$_{α$_{6}$}$(5 , 6 | V ) 〈 T f − α$_{1}$ 1 f α$_{2}$ 2 f − α$_{3}$ 3 f α$_{4}$ 4 f − α$_{5}$ 5 f α$_{6}$ 6 〉 ir 0 . from V we shall obtain the other property: From Fig. 3 and Fig. 10 it is possible to demonstrate the following equation: If we take into account only the explicit dependence of the functional Y ′ of interaction constant V without consid- ering the dependence of the full Green’s functions G $^{c}$( V ) Because of the necessity to have the functional derivatives over mass operator Σ we shall use the Dyson equation (15) rewritten in the form [ x = ( α, x , σ, τ )]: V β dY ′ dV | G c = ∑ α$_{1}$α$_{2}$ ∑ 12 G c α$_{1}$$_{α$_{2}$}$(2 , 1 | V )Σ$_{α}$$_{1}$$_{α}$$_{2}$(1 , 2 | V ) = T r [ ˆ Σ ˆ G $^{c}$] . (21) δβY ′ δG$_{α}$$_{1}$$_{α}$$_{2}$ (1 , 2) = α$_{1}$α$_{2}$ 2 V $^{2}$Λ$_{α}$$_{2}$$_{α}$$_{1}$ (2 , 1) = 1 2 Σ$_{α}$$_{2}$$_{α}$$_{1}$(2 , 1) . (20) G c (0) − $^{1}$( x, x $^{′}$) = G c − $^{1}$( x, x $^{′}$) + Σ( x, x $^{′}$) (22)