A linear realization of flavor SU (3) × SU (3) symmetry is developped with scalar and pseudoscalar mesons coupled to baryons and massive vector fields. This system may be also coupled to colored quarks and gluons, which are expected to be deconfined above a critical range of energy densities and seemingly inside baryons. The coupling to vector fields may lead to finite density baryonic and also anti-baryonic matter. Prescriptions for the stability equation which yields bound systems is verified. A qualitative discussion of the possible resulting (QCD - type) phase diagram is discussed including the possibility of finding several kinds of superfluid (and eventually superconductive) states. Some bosonic fields are assumed to have non zero expected values, at least at low energies, corresponding to dynamical symmetry breakings. A generalized symmetry radius is found and the masses of the particles are found to vary with density. Possible relevance to relativistic heavy ion collision is pointed out.
