  Properties of the weakly non-ideal Bose gas are considered without suggestion
on C-number representation of the creation and annihilation operators with zero
momentum. The "density-density" correlation function and the one-particle Green
function of the degenerated Bose gas are calculated on the basis of the
self-consistent Hartree-Fock approximation. It is shown that the spectrum of
the one-particle excitations possesses a gap whose value is connected with the
density of particles in the "condensate". At the same time, the pole in the
"density-density" Green function determines the phonon-roton spectrum of
excitations which exactly coincides with one discovered by Bogolyubov for the
collective excitations (the "bogolons").
