Necessary conditions for microscopic many-body theories

Familiar necessary conditions for the saturation of many-body binding energies are reconsidered in order to provide a better understanding of the analyticity properties of the ground state energy and of the convergence properties of certain sums of Goldstone diagrams. Using these results and other elementary arguments, we identify a minimum class of diagrams which must be summed to all orders if the perturbative treatment of other diagrams is to converge