Covariant density functional theory plays an important role in describing many phenomena in nuclear structure physics. However, so far, the parameters of these functionals are determined in a completely phenomenological way. On the way to ab-initio derivations of such functionals, we plan to use relativistic Brueckner-Hartree-Fock theory. I will discuss in this talk investigations in symmetric and assymetric nuclear matter and first attempts to solve the corresponding equations for finite nuclei.

Inviter: Shan-Gui Zhou