A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations

TL;DR

This paper critically examines the renormalization process in Phi-derivable approximations, focusing on the existence of solutions and the nature of divergences in the self-consistent equations within the CJT formalism.

Contribution

It offers a new perspective on the renormalization of Phi-derivable approximations, emphasizing the solution's existence and divergence behavior in a specific truncation.

Findings

Some divergences do not appear at the solution level

Existence of solutions depends on the truncation and parameters

Ultraviolet divergences are subtle and may not manifest in the expected way

Abstract

We revisit the renormalization of Phi-derivable approximations from a slightly different point of view than the one which is usually followed in previous works. We pay particular attention to the question of the existence of a solution to the self-consistent equation that defines the two-point function in the Cornwall-Jackiw-Tomboulis formalism and to the fact that some of the ultraviolet divergences which appear if one formally expands the solution in powers of the bare coupling do not always appear as divergences at the level of the solution itself. We discuss these issues using a particular truncation of the Phi functional, namely the simplest truncation which brings non-trivial momentum and field dependence to the two-point function.