  We test a non equilibrium approach to study the behavior of a Bose-Fermi
mixture of alkali atoms in the presence of a Feshbach resonance between bosons
and fermions. To this end we derive the Hartree-Fock-Bogoliubov (HFB) equations
of motion for, the interacting system. This approach has proven very successful
in the study of resonant systems composed of Bose particles and Fermi
particles. However, when applied to a Bose-Fermi mixture, the HFB theory fails
to identify even the correct binding energy of molecules in the appropriate
limit. Through a more rigorous analysis we are able to ascribe this difference
to the peculiar role that bosonic depletion plays in the Bose-Fermi pair
correlation, which is the mechanism through which molecules are formed. We
therefore conclude that molecular formation in Bose-Fermi mixtures is driven by
three point and higher order correlations in the gas, unlike any other resonant
system studied in the context of ultra-cold atomic physics.
