Δ self-energy at finite temperature and density and the πn cross section

The self-energy of the Δ baryon is evaluated at a finite temperature and density using the real-time formalism of thermal field theory. The Dyson-Schwinger equation is used to get the exact thermal propagator followed by the spectral function of Δ. The πN scattering cross section obtained using an explicit Δ exchange is normalized to the experimental data in the vacuum, and its medium modification is implemented by means of the exact thermal propagator. A significant suppression of the peak of the cross section is observed at a higher temperature and baryon density. Effects on the mean relaxation time of nucleons and the temperature dependence of the shear viscosity of a pion nucleon gas are demonstrated.