Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram

Abstract

The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the $\phi^4$-theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the $\Phi$-derivable approximation or 2PI effective action concept.Comment: 18 pages, 7 figures Changes in version 2: Adapted title to the first paper of the series, added one figure and some references. This version was submitted to Phys. Rev. D; Changes in version 3: added one more reference Changes in version 4 (accepted for publication by Phys. Rev. D): Added a paragraph about the massless case and some remarks in the introductio