Nuclear matter in relativistic non-linear models

We have determined the equation of state of nuclear matter according to relativistic non-linear models. In particular, we are interested in regions of high density and/or high temperature, in which the thermodynamic functions have very different behaviours depending on which model one uses. The high-density behaviour is, for example, a fundamental ingredient for the determination of the maximum mass of neutron stars. As an application, we have studied the process of two-pion annihilation into e+e- pairs in dense and hot matter. Accordingly, we have determined the way in which the non-linear terms modify the meson propagators occurring in this process. Our results have been compared with those obtained for the meson propagators in free space. We have found models that give an enhancement of the dilepton production rate in the low invariant mass region. Such an enhancement is in good agreement with the invariant mass dependence of the data obtained in heavy ions collisions at CERN/SPS energies. (author)