Exact renormalization group and Phi-derivable approximations

TL;DR

This paper combines Phi-derivable approximations with the exact renormalization group to create efficient non-perturbative schemes, simplifying the hierarchy of flow equations and enabling practical solutions.

Contribution

It introduces a novel method that merges Phi-derivable approximations with the renormalization group, simplifying complex equations and providing new practical solution techniques.

Findings

Simplifies the hierarchy of RG flow equations using Phi-derivable approximations.

Transforms nonlinear equations into initial value problems for easier solving.

Provides a practical framework for non-perturbative analysis.

Abstract

We show that the so-called Phi-derivable approximations can be combined with the exact renormalization group to provide efficient non-perturbative approximation schemes. On the one hand, the Phi-derivable approximations allow for a simple truncation of the infinite hierarchy of the renormalization group flow equations. On the other hand, the flow equations turn the non linear equations that derive from the Phi-derivable approximations into an initial value problem, offering new practical ways to solve these equations.