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Connected diagrams and Keldysh

I have seen that: In the ground state ($T = 0$) formulation of the Green’s function written in terms of operators in the interaction picture, the Green’s function reads: $$G(r,t;r',t') = -i\frac{\...
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Why are the corrections to the effective Lagrangian (Wilsonian renormalization) given by connected diagrams only?

This question will fully refer to the presentation ref. 1, from which I'll take the numbering. Since it involves also diagrams and it appears as a fairly basic question about Wilsonian renormalization,...
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