  Starting from the full many-body Hamiltonian of interacting electrons the
effective self-energy acting on electrons residing in a subspace of the full
Hilbert space is derived. This subspace may correspond to, for example,
partially filled narrow bands, which often characterize strongly correlated
materials. The formalism delivers naturally the frequency-dependent effective
interaction (the Hubbard U) and provides a general framework for constructing
theoretical models based on the Green function language. It also furnishes a
general scheme for first-principles calculations of complex systems in which
the main correlation effects are concentrated on a small subspace of the full
Hilbert space.
