2PI functional techniques for abelian gauge theories

We summarize our recent work [U. Reinosa, J. Serreau, JHEP 0711 (2007) 097 [arXiv:0708.0971 [hep-th]]; U. Reinosa, J. Serreau, JHEP 0607 (2006) 028; See also Nucl. Phys. A 785 (2007) 230; U. Reinosa, J. Serreau, in preparation] concerning the formulation of two-particle-irreducible (2PI) functional techniques for abelian gauge field theories.