Symmetry properties and renormalization group in the stable superfluid phase of bosons at zero temperature

The appearence of divergences in perturbation theory for a system in a stable phase requires the existence of an underlying symmetry and related Ward identities to remove exactly these singularities in the physical response functions. In this paper we consider explicitly the Ward identities associated with the (gauge) symmetry of the interacting neutral Bose gas at zero temperature to solve the old-standing problem of infrared divergencies due to Bose- Einstein condensation. The exact infrared behavior of the system is achieved for any dimension d > 1. For 1 < d ? 3 the system is controlled by a non trivial line of fixed point distant from the Bogoliubov solution, while above d = 3 the Bogoliubov fixed point is found to be stable.