Self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the Δ distribution function

We derive the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) equation for the delta distribution function within the framework which we have done for nucleon's. In our approach, the Δ isobars are treated in essentially the same way as nucleons. Both mean field and collision terms of Δ's RBUU equation are derived from the same effective Lagrangian and presented analytically. We calculate the in-medium NΔ elastic and inelastic scattering cross sections up to twice nuclear matter density and the results show that the in-medium cross sections deviate substantially from Cugnon's parametrization that is commonly used in the transport model.