Many theoretical methods for N-electron systems use a reference state whose electronic density in general differs from that of the associated eigenstate. In contrast, the density functional theory of Kohn and Sham postulates a model reference system for which these two densities are identical. An alternative postulate, requiring the reference state to have maximum projection on the true wave function (the Brueckner-Brenig construction), is shown here to provide a theory in which the ground-state energy is a functional of the reference-state density. This revised formalism makes it possible to identify elements of the theory with specific formulas and concepts of formal many-body theory. In particular, the one-electron wave functions are in one-to-one correspondence with physical quasiparticles of a generalized Fermi-liquid theory, and the one-electron energies are Landau quasiparticle energies.