  In crystalline solids the acoustic phonon is known to be the
frequency-gapless Goldstone boson emerging from the spontaneous breaking of the
continuous Galilean symmetry induced by the crystal lattice. It has also been
described as the gauge boson that appears when the free electrons' Lagrangian
in the crystal is requested to be locally gauge invariant with respect to T(3),
the group of the infinitesimal spatial translations. However, the
non-Abelianity of T(3) makes the acoustic phonon a frequency-gapped mode, in
contradiction with its description as Goldstone boson. A different perspective
overcomes this contradiction. In fact, we show that both the acoustic and
optical phonon - the latter never appearing following the other two approaches
- emerge respectively as the gapless Goldstone (phase) and the gapped Higgs
(amplitude) fluctuation mode of an order parameter arising from the spontaneous
breaking of a global symmetry, without invoking the gauge principle. The
optical phonon's frequency-gap is present in all regimes, and it arises from a
mass-like term in the Lagrangian due to the Higgs mechanism itself. Instead, an
eventual acoustic phonon's frequency-gap appears only in the strong nonlinear
regime, and it is due to an anharmonic term, the same term arising from the
gauging of T(3), an approach which did not provide any description of the
optical phonon, though. In addition, the Higgs mechanism describes all the
phonon-phonon interactions, including a possible perturbation on the acoustic
phonon's frequency dispersion relation induced by the eventual optical phonon,
a peculiar behavior not described so far in these terms.
