  Off-shellness and inhomogeneities are in the non-equilibrium dynamics of the
lambda phi^4 model are studied using the closed timepath formalism reformulated
as kinetic field theory. We take into account initial correlations up to the
4-point functions. The model is shown to exhibit a SO(1,1) symmetry broken by
interactions and initial conditions. The divergence of the corresponding
Noethercurrent is calculated and the Ward-Takahashi relations for the broken
symmetry are given. They constitute a set of generalized integrated kinetic
equations for the general n-point functions. We demonstrate that
energy-momentum conservation follows from the transport equations. As an
application we discuss inhomogeneities and general non-equilibrium conditions
in the free field model. In our solution we identify the casimir-effect.
