2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/43419In this lecture we review recent progress in various aspects of non-equilibrium QFT with respect to relativistic heavy ion collisions. As a first and rather general study we summarize our (numerical) investigations for a dissipative quantum time evolution of $ϕ^4$-field theory for a spatially homogeneous system in 2+1 space-time dimensions on the basis of the Kadanoff-Baym equations. The initial conditions can be chosen arbitrarily and far from equilibrium. The calculations demonstrate how thermalization and chemical equilibration is achieved ab initio from the underlying QFT. As a possible candidate for a non-equilibrium phase transition phenomena we then adress the stochastic formation of disoriented chiral condensates. Finally we elaborate on a new 3+1 dimensional Monte Carlo parton cascade solving kinetic Boltzmann processes including inelastic multiplication processes (gg<->ggg) in an unified manner, where the back reaction channel is treated for the first time fully consistently.16 pages, 14 figures; invited talk at NATO Advanced Study Institute: Structure and Dynamics of Elementary Matter, Kemer, Turkey, 22 Sep - 2 Oct 2003; last chapter of this talk has also been presented by Z.Xu as a poster at the QM2004 conferenceHigh Energy Physics - Phenomenologytext