At the boundary between reduced density-matrix and density-functional theories

Here, we revisit the problem of finding the ground-state energy of an N-fermion fluid under an external field, with molecular structure as the ultimate target. Density-functional methods only have to deal with electron density, but require an empirical functional; reduced density-matrix methods involve a matrix on pair space and do give exact bounds, but require very complex linear programming to achieve their results. The polydensity representation that we introduce has the advantage of dealing only with densities, requires no empirical information, and also gives exact bounds; the major problem is that of accumulating and utilizing conditions on the densities that iteratively improve their realizability in the class of N-fermion systems. We indicate several directions along these lines and make some primitive applications. (C) 2005 American Institute of Physics.