We introduce an alternative approach to highly correlated systems that
generalizes the Fermi hypernetted chain and correlated basis function
techniques. While the latter approaches can be applied only to system
s for which a nonrelativistic wave function can be defined, the presen
t approach is based on the variation of a trial Hamiltonian within a p
ath-integral framework and thus can be applied also to relativistic an
d field theoretical problems. We derive a diagrammatic scheme for the
present approach and show how a particular choice of 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 ou
r approach can be used to find upper bounds to ground-state energies i
n systems that the Fermi hypernetted chain approach cannot handle, inc
luding those described by an energy-dependent effective Hamiltonian. W
e demonstrate our approach by applying it to a quantum field theoretic
al system of interacting pions and nucleons.