Developing Transport Theory to Study the Chiral Phase Transition

Chiral symmetry is an important aspect of QCD. Modelling this via the Nambu-Jona-Lasinio model, we construct a complete relativistic transport theory for quarks and mesons. The collision integral is analysed in a systematic 1/N_c approximation, and via this, it is shown that one can naturally incorporate mesonic degrees of freedom plus the hadronization of quarks and antiquarks into mesons into the field theoretic description. Time permitting, some simulation results, on the level of the Vlasov equation and also including collisions in a relaxation time approach, will be discussed.