We introduce a new approach to highly correlated systems which generalizes
the Fermi Hypernetted Chain and Correlated Basis Function techniques. While the
latter approaches can only be applied to systems for which a nonrelativistic
wave function can be defined, the new approach is based on the variation of a
trial hamiltonian within a path integral framework and thus can also be applied
to relativistic and field theoretical problems. We derive a diagrammatic scheme
for the new approach and show how a particular choice of the trial hamiltonian
corresponds exactly to the use of a Jastrow correlated ansatz for the wave
function in the Fermi Hypernetted Chain approach. We show how our new approach
can be used to find upper bounds to ground state energies in systems which the
FHNC cannot handle, including those described by an energy-dependent effective
hamiltonian. We demonstrate our approach by applying it to a quantum field
theoretical system of interacting pions and nucleons.Comment: 35 RevTeX pages, 7 separated ps figures available on reques
