Rigorous approach to the problem of ultraviolet divergencies in dilute Bose gases

Abstract

We have found an expression for the full many-body Green's function of N pairwise finite-range interacting atoms, in a form of a chain fraction involving two-body T-matrices only, with no explicit presence of the interaction potentials themselves. We show that in the limit of infinitely small potential range, this expression reduces to the Green's function for N atoms interacting via a generalized pseudo-potential, function of a free parameter \Lambda. Using this \Lambda-freedom we resolve all inconsistensies of the Hartree-Fock-Bogoliubov formalism known so far, with no ad hoc modifications of the theory.