Relativistic transport theory for $N$, $\Delta$ and $N^{*}$(1440) system
  A self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the $N^{*}$(1440) resonance is developed based on an effective Lagrangian of baryons interacting through mesons.   The equation is consistent with that of nucleon's and delta's which we derived before. Thus, we obtain a set of coupled equations for the $N$, $\Delta$ and $N^{*}$(1440) distribution functions.   All the $N^{*}$(1440)-relevant in-medium two-body scattering cross sections within the $N$, $\Delta$ and $N^{*}$(1440) system are derived from the same effective Lagrangian in addition to the mean field and presented analytically. Medium effects on the cross sections are discussed. 
Guangjun Mao, L. Neise, H. St\"ocker, W. Greiner