  In this article we study the time evolution of an interacting field
theoretical system, i.e. \phi^4-field theory in 2+1 space-time dimensions, on
the basis of the Kadanoff-Baym equations for a spatially homogeneous system
including the self-consistent tadpole and sunset self-energies. We find that
equilibration is achieved only by inclusion of the sunset self-energy.
Simultaneously, the time evolution of the scalar particle spectral function is
studied for various initial states. We also compare associated solutions of the
corresponding Boltzmann equation to the full Kadanoff-Baym theory. This
comparison shows that a consistent inclusion of the spectral function has a
significant impact on the equilibration rates only if the width of the spectral
function becomes larger than 1/3 of the particle mass. Furthermore, based on
these findings, the conventional transport of particles in the on-shell
quasiparticle limit is extended to particles of finite life time by means of a
dynamical spectral function A(X,\vec{p},M^2). The off-shell propagation is
implemented in the Hadron-String-Dynamics (HSD) transport code and applied to
the dynamics of nucleus-nucleus collisions.
