  It is argued that the recently observed Fermi liquids in strongly interacting
ultracold Fermi gases are adiabatically connected to a projected Fermi gas.
This conclusion is reached by constructing a set of Jastrow wavefunctions,
following Tan's observations on the structure of the physical Hilbert space
[Annals of Physics 323, 2952 (2008)]. The Jastrow projection merely implements
the Bethe-Peierls condition on the BCS and Fermi gas wavefunctions. This
procedure provides a simple picture of the emergence of Fermi polarons as
composite fermions in the normal state of the highly polarized gas. It is also
shown that the projected BCS wavefunction can be written as a condensate of
pairs of composite fermions (or Fermi polarons). A Hamiltonian for the
composite fermions is derived. Within a mean-field theory, it is shown that the
ground state and excitations of this Hamiltonian are those of a non-interacting
Fermi gas although they are described by Jastrow-Slater wavefunctions.
