In this lecture note we address the dynamics of strongly interacting
relativistic fields within the theory of Kadanoff and Baym and compare
to the corresponding relativistic on-shell Boltzmann limit. As an example all
expressions are given explicitly for the scalar Φ4-theory and numerical solutions
are discussed in case of weak and strong coupling for Φ4-theory in 2+1 dimensions.
Furthermore, the Kadanoff-Baym equations are expanded in first order
gradients in phase space and off-shell transport equations are derived in the
Botermans-Malfliet scheme for the Wightman function G<(x, p). Finally, a generalized
testparticle Ansatz ist introduced for the real quantity iG<(x, p) which
leads to transparent equations of motion for the testparticles and allows to solve
the off-shell transport equations also for (moderately) inhomogeneous systems.
Keywords: strongly coupled systems, nonequilibrium dynamics
