Irreducible vertex part

Having reduced all quantities to their vertex irreducible parts we can introduce the screened interaction. In each order of the loop expansion we have to resum a series of diagrams. For instance, the series of one loop graphs... 

Fig. 5-16- Structure of a general diagram contribution to J7 ftp], The filled parts are vertex-irreducible...

The argument exploits the fact that in each diagram contributing to Ifi a we can uniquely identify some distinguished vertex irreducible part. It is easily transferred to any quantity showing that property. Consider for instance Cp(n)j expressed in terms of the set of diagrams with one open line ... 

A I-reducible diagram is made of p I-irreducible parts and of interaction lines connecting these irreducible parts. Each I-irreducible part is considered as an m-leg vertex (nt 0, see Fig. 10.18), when m interaction lines connect this irreducible part to other irreducible parts. The corresponding tree has no external legs (see Fig. 10.15) consequently, its p vertices are connected by (p - 1) interaction lines. Each vertex of the skeleton tree can be labelled by an index j (j = l,...,p). Here, the symbol m, represents the number of legs of... 

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