ρ self-energy at finite temperature and density in the real-time formalism

The ρ meson self-energy in nuclear matter from baryonic loops is analysed in the real-time formulation of field theory at finite temperature and density. The discontinuities across the branch cuts of the self-energy function are evaluated for an exhaustive set of resonances in the loops considering the fully relativistic thermal baryon propagator including anti-baryons. Numerical calculations show a significant broadening of the ρ spectral function coming from the Landau cut. Adding the contribution from mesonic loops, the full spectral function of the ρ in a thermal gas of mesons, baryons and anti-baryons in equilibrium is evaluated at various values of temperature and baryonic chemical potential.