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.

Symmetry energy coefficients of asymmetric nuclear matter generalized are investigated as the inverse of nuclear matter polarizabilities with two different approaches. Firstly a general calculation shows they may depend on the neutron-proton asymmetry itself. The choice of particular prescriptions for the density fluctuations lead to certain isospin (n-p asymmetry) dependences of the polarizabilities. Secondly, with Skyrme type interactions, the static limit of the dynamical polarizability is investigated corresponding to the inverse symmetry energy coefficient which assumes different values at different asymmetries (and densities and temperatures). The symmetry energy coefficient (in the isovector channel) is found to increase as n-p asymmetries increase. The spin symmetry energy coefficient is also briefly investigated.