  We discuss the standard approach to the problem of the low momentum limit of
the spectrum for a weakly interacting Bose gas. The Bogoliubov's spectrum is
shown to be obtained as a Goldstone mode thanks to the introduction of a
chemical potential $\mu$. This procedure has, however, difficulties since the
breaking of the gauge symmetry implies that the corresponding chemical
potential must be taken as zero, unless it is introduced before breaking the
symmetry. But if this is done, after the symmetry breaking $\mu$ loses its
meaning as a chemical potential. An alternative two-mode solution is suggested
having two modes, one of them being the free-particle quadratic in momentum
spectrum, the second bearing a gap. This gap leads to a $\lambda$-type behavior
of the specific heat near the critical temperature.
