Functional renormalization group and 2PI effective action formalism

We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, other functional renormalization group (fRG), in an effort to develop new approximations for field theoretical description of strongly coupled systems. In particular, we exploit exact 2PI relations between two-point and four-point functions order truncate infinite hierarchy equations group. The truncation is "exact" ways. First, solution resulting flow equation independent choice regulator. Second, this coincides with that functions, any selection two-skeleton diagrams characterizing a so-called $\Phi$-derivable approximation. transformation formalism into offers ways solve these practice, provides insight certain aspects their renormalization. It also opens possibility approximation schemes going beyond strict ones, as well fRG hierarchy.