Low-frequency asymptotic form of the self-energy parts of a superfluid Bose system at T=0

A functional integration method is used to obtain the first two terms of the asymptotic form of the Green's functions at (..omega..,k) =p..-->..0 and the principal asymptotic terms of the self-energy parts of three-dimensional and two-dimensional superfluid Bose systems at T=0. It is shown that the anomalous self-energy part tends to zero like (ln Rp)/sup -1/ for three-dimensional system and like p for the two-dimensional system.