Renormalizability of Φ-derivable approximations in scalar φ4 theory

We discuss the renormalizability of Phi-derivable approximations in scalar phi(4) theory in four dimensions. The formalism leads to self-consistent equations for the 2-point and the 4-point functions which are plagued by ultraviolet divergences. Through a detailed analysis of the one and two-loop self-energy skeletons, we show that both equations can be renormalized simultaneously and determine the corresponding counterterms. These insure the elimination of ultraviolet divergences both at zero and finite temperature. (C) 2003 Elsevier B.V. All rights reserved.