German Title: Transporttheorie für skalare Quarks und Gluonen

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Translation of abstract (English)

In this work, we have detailed the calculations of the transport and constraint equations for a theory of scalar quarks and gluons with self-interactions. Special care has been taken in particular in understanding how the transport equation, taken on its own, leads to a Boltzmann-like equation when considered in the quasiparticle approximation. Through the analysis of all self-energy graphs that occur it is evident which role they play: certain graphs give rise to the expected cross sections, while others serve to renormalize diagrams of lower order scattering processes. In the calculation of the transport equation, so-called pinch singularities arise in individual self-energy diagrams. We demonstrate explicitly how they cancel in equilibrium. For the case of non-equilibrium, several ansätze are investigated, but none of them leads to the cancellation of all pinch singularities. Finally, the constraint equation is considered. This leads to the introduction of a finite width into the propagators. The main advantage of this is that no pinch singularities can possibly occur. The disadvantage, however, is that the calculations become very cumbersome and it is no longer straightforward to cast the transport equation into a form which can be recognized as being Boltzmann-like.