  We investigate nuclear matter properties in the relativistic Brueckner
approach. The in-medium on-shell T-matrix is represented covariantly by five
Lorentz invariant amplitudes from which we deduce directly the nucleon
self-energy. We discuss the ambiguities of this approach and the failure of
previously used covariant representations in reproducing the nucleon
self-energies on the Hartree-Fock level. To enforce correct Hartree-Fock
results we develop a subtraction scheme which treats the bare nucleon-nucleon
potential exactly in accordance to the different types of meson exchanges. For
the remaining ladder kernel, which contains the higher order correlations, we
employ then two different covariant representations in order to study the
uncertainty inherent in the approach. The nuclear matter bulk properties are
only slightly sensitive on the explicit representation used for the kernel.
However, we obtain new Coester lines for the various Bonn potentials which are
shifted towards the empirical region of saturation. In addition the nuclear
equation-of-state turns out to be significantly softer in the new approach.
