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

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.

30 pages, 12 figures

References in corpus (5)

• Exact renormalization group and Phi-derivable approximations
• Renormalized Finite Temperature phi^4 theory from the 2PI Effective Action
• Broken phase scalar effective potential and Phi-derivable approximations
• Topological defect formation from 2PI effective action techniques
• Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation

Cited by in corpus (9)

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• Broken phase effective potential in the two-loop Phi-derivable approximation and nature of the phase transition in a scalar theory
• Localized rainbows in the QCD phase diagram
• The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations
• Loss of solution in the symmetry improved Phi-derivable expansion scheme
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• The $O(4)$ ${\varphi }^4$ model as an effective light meson theory: A lattice-continuum comparison