A practical method is suggested for performing renormalized 2 particle irreducible (2PI) resummation at finite temperature using specific renormalization schemes. I examine the consistency of such schemes in the paper. Advantages of the proposed method are that there is no need to solve Bethe-Salpeter equations for 2PI resummation, and there is no explicit diagrammatic resummation of the 2 particle reducible graphs. The proposed method is used to perform a two-loop renormalized 2PI resummation in the finite temperature ${\Phi }^4$ model.

• Received 20 December 2006

DOI:https://doi.org/10.1103/PhysRevD.76.125004