In the framework of pionless nucleon–nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle–particle, hole–hole, and particle–hole pairs. We focus on the problem of finding a suitable starting point for perturbative calculations near the unitary limit (kFa)→∞ and (kFr)→0, where kF is the Fermi momentum, a is the scattering length and r is the effective range. We try to clarify the relationship between different classes of diagrams and the large g and large D approximations, where g is the fermion degeneracy and D is the number of space–time dimensions. In the large D limit we find that the energy per particle in the strongly interacting system is 1/2 the result for free fermions.