one-electron Green’s function ${\bf G}$. The functional $\Omega[{\bf G}]$ can be shown to be stationary at the physical ${\bf G}$. In principle, this is an exact variational approach which provides information not only on static equilibrium but also on dynamic excitation properties. The functional dependence $\Omega[{\bf G}]$, however, is generally not known explicitly as it must be constructed by summation of an infinite series of renormalized skeleton diagrams. In the standard approximation the exact but unknown functional is replaced by an explicitly known but approximate one which is based on an incomplete summation of the diagram series. This leads to the well-known perturbational (“conserving”) theories. [@BK61] Higher-order approaches as the fluctuation-exchange approximation [@BSW89] are mainly applied to discrete lattice models while for continuum systems, e.g. for the inhomogeneous electron gas, one has to be content with lowest-order theories as the GW method. [@SMH80; @SMH82; @AG98]

A second type of general methods is based on density-functional (DF) approaches. [@HK64; @KS65] Normally these aim at the inhomogeneous electron gas but can also be applied to Hubbard-type lattice models. [@SGN95] Compared with the Green’s-function formalism, there is a conceptually similar situation for DF approaches: In the latter the ground-state energy $E$ (or the 