  The BEC regime of a cold fermi gas is characterised by coupled atoms (dimers)
which, superficially, look like elementary bosons. We examine how
simply-bosonic they really are; firstly, in the Bogoliubov approximation and
further, through new actions for the BEC regime in which dimers are represented
by coupled Gross-Pitaevskii fields. We find identity at the level of the
Bogoliubov approximation in the deep BEC regime, permitting a simple
Gross-Pitaevskii description. This fails rapidly as we move towards the BCS
regime. However, even in the deep BEC regime there is an intrinsic difference
if we go beyond the Bogoliubov approximation. To exemplify this we construct
vortex solutions.
