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In this paper we derive a hierarchy of integral equations from the 4PIeffective action which have the form of Bethe-Salpeter equations. We show that,together with the equation of motion for the self-consistent 4-vertex, theseintegral equations are closed, and that their expansions give infinite seriesof connected diagrams which have the correct symmetry.

Bethe-Salpeter Equations from the 4PI effective action