Isospin effects in intermediate energy heavy ion collisions

We investigate the density dependence of the symmetry energy in a relativistic description by decomposing the iso-vector mean field into contributions with different Lorentz properties. We find important effects of the iso-vector, scalar $\delta$ channel on the density behavior of the symmetry energy. Finite nuclei studies show only moderate effects originating from the virtual $\delta$ meson. In heavy ion collisions from Fermi to relativistic energies up to $1-2 AGeV$ one finds important contributions on the dynamics arising from the different treatment of the microscopic Lorentz structure of the symmetry energy. We discuss a variety of possible signals which could set constraints on the still unknown density dependence of the symmetry energy, when experimental data will be available. Examples of such observables are isospin collective flow, threshold production of pions and kaons, isospin equilibration and stopping in asymmetric systems like $Au+Au$, $Sn+Sn$ and $Ru(Zr)+Zr(Ru)$.