a certain subspace of trial self-energies. Trial self-energies must be representable within an exactly solvable reference system sharing the same interaction with the original system.

This result has important consequences as it opens a route for constructing a novel class of approximations. Although the self-energy essentially contains the same information as the Green’s function or the (time-dependent) density, the new approach is conceptually contrary to the Green’s-function approach and to the DF approach as there is no approximation to be tolerated for the central functional. Instead of approximating the functional itself, it is considered on a restricted domain. The self-energy-functional approach is completely general and yields approximations which are non-perturbative, thermodynamically consistent and systematic. Opposed to numerical techniques directly applied to systems of finite size, the self-energy-functional approach provides a variational or self-consistent embedding of finite systems and thus yields results in the thermodynamical limit. Such techniques are needed to construct phase diagrams from standard correlated lattice models. A potentially fruitful field of application are systems with competing types of order resulting from spin, charge or orbital correlations as it is typical e.g. for numerous transition-metal oxides. [@OM00; @Geb97; @BDN01]

In the present paper the approach is introduced and a 