  Theory of a weakly non-ideal Bose gas in the canonical ensemble is developed
without assumption of the C-number representation of the creation and
annihilation operators with zero momentum. It is shown that the pole of the
"density-density" Green function exactly coincides with the Bogolybov's
phonon-roton spectrum of excitations. At the same time in the one-particle
excitation spectrum a gap exists. The value of this gap is connected with the
density of particles in the "condensate".
