  A model of scalar gluons and scalar quarks that successfully gives a ln s
behavior in high energy qq scattering and which contains a three gluon vertex
is used to derive transport equations for the quarks and gluons. Quasiparticle
and semiclassical approximations are utilized. In particular, the collision
integral is studied. At first the terms are organized according to the number
of gluon exchange interactions, and it is shown explicitly that the occurrence
of all two body differential scattering cross sections in the Boltzmann
equation requires an evaluation of all terms to this order. One obtains qg->
qg, q bar q->gg, qq->qq, and q bar q -> q bar q. An additional ordering
according to the inverse number of colors reveals that the quark loop diagrams
are suppressed, and diagrams that lead to gluon production or scattering
dominate. The self energy with three gluons exchanged is then examined. From
this, it is evident that initial as well as final state interactions enter into
a generalized collision integral. The generalized Boltzmann-like equation
involving n gluon exchange for quark transport is given.
