A Quark Transport Theory to describe Nucleon--Nucleon Collisions

On the basis of the Friedberg-Lee model we formulate a semiclassical transport theory to describe the phase-space evolution of nucleon-nucleon collisions on the quark level. The time evolution is given by a Vlasov-equation for the quark phase-space distribution and a Klein-Gordon equation for the mean-field describing the nucleon as a soliton bag. The Vlasov equation is solved numerically using an extended testparticle method. We test the confinement mechanism and mean-field effects in 1+1 dimensional simulations.