BOSONIZATION OF COUPLED ELECTRON-PHONON SYSTEMS

We calculate the single-particle Green's function of electrons that ar e coupled to acoustic phonons by means of higher dimensional bosonizat ion. This non-perturbative method is not based on the assumption that the electronic system is a Fermi liquid. For isotropic three-dimension al phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electr on-phonon coupling the quasi-particle residue is small. We also show t hat Luttinger liquid behavior in three dimensions can be due to quasi- one-dimensional anisotropy in the electronic band structure or in the phonon frequencies.