  The BCS to BEC crossover in attractive Fermi systems is a prototype of weak
to strong coupling evolution in many body physics. While extensive numerical
results are available, and several approximate methods have been developed,
most of these schemes are unsuccessful in the presence of spatial
inhomogeneity. Such situations call for a real space approach that can handle
large spatial scales and retain the crucial thermal fluctuations. With this in
mind, we present comprehensive results of a real space auxiliary field approach
to the BCS to BEC crossover in the attractive Hubbard model in two dimensions.
The scheme reproduces the Hartree-Fock-Bogoliubov ground state, and leads to a
$T_c$ scale that agrees with quantum Monte Carlo estimates to within a few
percent. We provide results on the $T_c$, amplitude and phase fluctuations,
density of states, and the momentum resolved spectral function over the entire
interaction and temperature window. We suggest how the method generalises
successfully to the presence of disorder, trapping, and population imbalance.
