  At large number of colors, N_c quarks in baryons are in a mean field of
definite space and flavor symmetry. We write down the general Lorentz and
flavor structure of the mean field, and derive the Dirac equation for quarks in
that field. The resulting baryon resonances exhibit an hierarchy of scales: The
crude mass is O(N_c), the intrinsic quark excitations are O(1), and each
intrinsic quark state entails a finite band of collective excitations that are
split as O(1/N_c). We build a (new) theory of those collective excitations,
where full dynamics is represented by only a few constants. In a limiting (but
unrealistic) case when the mean field is spherically-and flavor-symmetric, our
classification of resonances reduces to the SU(6) classification of the old
non-relativistic quark model. Although in the real world N_c is only three, we
obtain a good accordance with the observed resonance spectrum up to 2 GeV.
