The partition function and the subsidiary conditions in the Bohm-Pines and Migdal-Galitsky’s supplementary variables method

Abstract

The supplementary variables method is applied to the approximate calculation of the partition function ofN interacting fermions. It is shown that the supplementary variables method in its original formulation due to Bohm-Pines and Migdal-Galitsky leads to wrong results. One obtains correct results if one assumes a modification, due to Kanazawa, of the subsidiary conditions in this method.