Developing Transport Theory to Systematically Include Mesons And Hadronization

Transport theory for the Nambu--Jona-Lasinio (NJL) model is examined. The collision term is investigated in a first approach in a coupling strength expansion. It can be demonstrated that this leads to a form easily recognized from the Boltzmann equation if the quasiparticle approximation is used. It is seen that enforcing a quasiparticle approximation suppresses the three body creation and annihilation processes that would otherwise be present. Including mesons and hadronization consistently in a $1/N_c$ expansion is discussed briefly. Some comments on the numerical simulation of the Vlasov equation and the relaxation time approximation to the collision term are made