We use a bosonization approach to calculate the single-particle Green's
function G(r,τ) 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→3 the
quasi-particle residue vanishes as
Z∝exp[−2π(d−3)1(mcκ)2], where
κ 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
γ⊥=6π1(mcκ)2. For d<3 we
find that G(r,0) decays exponentially at large distances.Comment: RevTex, no figures