  A straightforward expansion of Edwards' functional integral representation of
the grand partition function for a polymer liquid as an infinite set of Feynman
diagrams is shown to yield a cluster expansion that is closely related to the
corresponding Mayer cluster expansion developed for flexible molecules by
Chandler and coworkers. The procedure initially yields a perturbative cluster
expansion in which all free energies and correlation functions are expressed
diagrammatically as functionals of single-molecule correlation functions of
non-interacting molecules. Topological reduction yields several renormalized
expansions for collective correlation functions of all orders as functionals of
single-molecule correlation functions in the interacting fluid. Renormalized
expansions are also obtained for a generalized Ornstein-Zernicke (OZ) direct
correlation function and for intramolecular correlation functions. The
application of the formalism to coarse-grained models of polymer fluids is
discussed, and a loop expansion about self-consistent field theory is shown to
converge for sufficiently coarse-grained models, in which monomers are strongly
overlapping. The formalism is used to derive a new expression for the OZ direct
correlation function and to recover known results for the 2-point
intramolecular correlation function to first order in a loop expansion, for
binary blends and diblock copolymer melts.
