  Confined quantum systems involving $N$ identical interacting fermions are
found in many areas of physics, including condensed matter, atomic, nuclear and
chemical physics. In a previous series of papers, a manybody perturbation
method that is applicable to both weakly and strongly-interacting systems of
bosons has been set forth by the author and coworkers. A symmetry invariant
perturbation theory was developed which uses group theory coupled with the
dimension of space as the perturbation parameter to obtain an analytic
correlated wave function through first order for a system under spherical
confinement with a general two-body interaction. In the present paper, we
extend this formalism to large systems of fermions, circumventing the numerical
demands of applying the Pauli principle by enforcing the Pauli principle on
paper. The method does not scale in complexity with $N$ and has minimal
numerical cost. We apply the method to a unitary Fermi gas and compare to
recent Monte Carlo values.
