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

我们结合了两种非微扰方法，一种基于双粒子不可约 (2PI) 作用，另一种基于功能重整化组 (fRG)，以努力开发新的非微扰近似，用于强场理论描述耦合系统。特别是，我们利用两点和四点函数之间的精确 2PI 关系来截断函数重整化群的方程的无限层次。截断在两个方面是“精确的”。首先，所得流量方程的解与调节器的选择无关。其次，该解与两点和四点函数的 2PI 方程的解一致，对于表征所谓的两个骨架图的任何选择$\Phi$-可推导的近似值。将 2PI 形式的方程转换为流动方程提供了在实践中求解这些方程的新方法，并提供了对其重整化的某些方面的新见解。它还开启了开发超越严格的近似方案的可能性。$\Phi$-可推导的，以及 fRG 层次结构的新截断方案。