Relativistic direct Urca processes in cooling neutron stars

We derive a relativistic expression for neutrino energy losses caused by the direct Urca processes in degenerate baryon matter of neutron stars. We use two different ways to calculate the emissivity caused by the reactions to our interest. First we perform a standard calculation by Fermi's ''golden'' rule. The second calculation, resulting in the same expression, is performed with the aid of polarization functions of the medium. Our result for neutrino energy losses strongly differs from previous non-relativistic results. We also discuss nonconservation of the baryon vector current in reactions through weak charged currents in the medium, when the asymmetry between protons and neutrons is considered. The above effects, not discussed in the literature before, substantially modify the polarization functions responsible for the induced weak charged currents in baryon matter.