The Luttinger-Ward method applied to the 2D Coulomb gas

We review the Luttinger–Ward method and show how one can combine it with the theory of Baym and Kadanoff in order to get conserving approximations in many‐body perturbation theory. We solve the variation procedure numerically using an ansatz for the selfenergy in the case of the two‐ dimensional Coulomb problem. Comparison with results of the traditional iteration of the selfconsistency equation yields satisfactory agreement for parameters where the iteration converges. The extremalization of the Luttinger–Ward functional works beyond that point. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)