  We bosonize a Fermi liquid in any number of dimensions in the limit of long
wavelengths. From the bosons we construct a set of coherent states which are
related with the displacement of the Fermi surface due to particle-hole
excitations. We show that an interacting hamiltonian in terms of the original
fermions is quadratic in the bosons. We obtain a path integral representation
for the generating functional which in real time, in the semiclassical limit,
gives the Landau equation for sound waves and in the imaginary time gives us
the correct form of the specific heat for a Fermi liquid even with the
corrections due to the interactions between the fermions. We also discuss the
similarities between our results and the physics of quantum crystals.
