  We have investigated the attractive Hubbard model in the low density limit
for the 2D square lattice using the ladder approximation for the vertex
function in a self-consistent, conserving formulation. In the parameter region
where the on-site attraction is of the order of the bandwidth, we found no
evidence of a pseudo gap. Further, we have observed that the suppression of the
Fermi surface known to destroy superconductivity in one and two dimensions,
when these systems are treated using a non self-consistent theory
(Schmitt-Rink, et al., Phys. Rev. Lett. 63, 445 (1989)), does not occur when
pair-pair interactions are included. However, we do find a quasiparticle
lifetime that varies linearly with temperature, similar to many experiments.
Thus, although this system has a Fermi surface, it shows non Fermi liquid type
behaviour over a wide temperature range. We stress that our work uses thermal
Green's functions along the real time axis, and thus allows for a more accurate
determination of the dynamical properties of a model than theories that require
extrapolations from the imaginary frequency axis.
