  It is a well known fact that Dirac phenomenology of nuclear forces predicts
the existence of large scalar and vector mean fields in matter. To analyse the
relativistic self-energy in a model independent way, modern high precision
nucleon-nucleon ($NN$) potentials are mapped on a relativistic operator basis
using projection techniques. This allows to compare the various potentials at
the level of covariant amplitudes were a remarkable agreement is found. It
allows further to calculate the relativistic self-energy in nuclear matter in
Hartree-Fock approximation. Independent of the choice of the nucleon-nucleon
interaction large scalar and vector mean fields of several hundred MeV
magnitude are generated at tree level. In the framework of chiral EFT these
fields are dominantly generated by contact terms which occur at next-to-leading
order in the chiral expansion. Consistent with Dirac phenomenology the
corresponding low energy constants which generate the large fields are closely
connected to the spin-orbit interaction in $NN$ scattering. The connection to
QCD sum rules is discussed as well.
