Functional renormalization group and 2PI effective action formalism

TL;DR

This paper integrates the 2PI effective action and functional renormalization group methods to create exact, regulator-independent non-perturbative approximations for strongly coupled quantum field systems, enhancing solution techniques and renormalization insights.

Contribution

It introduces a novel approach combining 2PI and fRG formalisms, enabling exact, regulator-independent solutions and new approximation schemes for strongly coupled systems.

Findings

Exact, regulator-independent solutions for 2PI and fRG equations.

New methods for solving 2PI equations in practice.

Potential development of advanced truncation schemes.

Abstract

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.