  We discuss mean field theory of Quarkyonic matter at zero temperature. We
treat the nucleons with contact interactions in mean field approximation,
discussing both vector and scalar mean field interactions. We treat the quarks
without mean field vector interactions, but allow mass terms to be generated
consistent from a scalar mean field consistent with the additive quark model
for quark masses. Quarkyonic matter is composed of a shell of nucleons that
under-occupy the total available phase space associated with the underlying
quark degrees of freedom. The fully occupied Fermi sphere beneath this shell of
nucleons at high densities is thought of as quarks, but when this fully
occupied distribution of states first appears, although the phase space is
filled, the matter is at low density. For the transition between this low
density and high density saturated matter, we advocate a dual description of
the fully filled Fermi sea in terms of hadrons, and make a phenomenological
hypothesis for the equation of state of this matter. We then proceed to an
example where the mean field interactions are all vector and only associated
with the nucleons, ignoring the effects of mass change associated with the
scalar interactions. Except for the effects of Pauli blocking, the nucleons and
quarks do not interact. To get a reasonable transition to Quarkyonic matter the
interaction of the quarks among themselves are assumed to be non-perturbative,
and a simple phenomenological relation between quark Fermi energy and density
is introduced.

Nuclear Theory;High Energy Physics - Phenomenology