Counterterm resummation for 2PI-approximation in constant background

Explicit counterterm construction is presented in a symmetry breaking background for the 2PI effective action of the self-interacting one-component scalar field including skeleton diagrams to O(lambda(2)). The applied strategy is an extension of our treatment of the 2PI-Hartree approximation [G. Fejos, A. Patkos, Zs. Szep, Nucl. Phys. A 803 (2008) 135, arXiv: 0711.2933]. The procedure is also applied to the O(N) model

Renormalization and resummation in finite temperature field theories

Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of counterterms: one is a direct method where the necessary counterterms are constructed order by order; the other is a general one, based on renormalization group arguments. We demonstrate at one hand that, in mass independent schemes, mass resummation can be performed by gap equations renormalized prior to the substitution of the resummed mass for its argument. On the other hand it is shown that any (momentum-independent) form of mass and coupling constant resummation is compatible with renormalization, and one can explicitly construct the corresponding counterterms.Comment: 10 pages, 4 figures, revtex