  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.
