  We use a bosonization approach to calculate the single-particle Green's
function $G ( {\bf{r}} , \tau )$ of non-relativistic fermions coupled to
transverse gauge-fields in arbitrary dimension $d$. We find that in $d>3$
transverse gauge-fields do not destroy the Fermi liquid, although for $d < 6$
the quasi-particle damping is anomalously large. For $d \rightarrow 3$ the
quasi-particle residue vanishes as
  $Z \propto \exp [ - \frac{1}{2 \pi ( d-3)} (\frac{ \kappa}{mc } )^2 ]$, where
$\kappa$ is the Thomas-Fermi wave-vector, $m$ is the mass of the electrons, and
$c$ is the velocity of the gauge-particle. In $d=3$ the system is a Luttinger
liquid, with anomalous dimension
  $\gamma_{\bot} = \frac{1}{6 \pi} ( \frac{ \kappa}{mc} )^2$. For $d < 3$ we
find that $G ({\bf{r}} , 0 )$ decays exponentially at large distances.
