  In this thesis we develop a novel approximation scheme (eQPA), where the
effects of nonlocal coherence are included in the kinetic approach to
nonequilibrium quantum dynamics. The key element in our formalism is the
finding of new singular shell solutions, located at $k_{0,z} = 0$ in the phase
space of 2-point Wightman function, which describe the nonlocal quantum
coherence between the ``opposite'' mass-shell excitations for spatially
homogeneous and static planar symmetric problems, respectively. This phase
space structure leads to a closed set of transport equations for the
corresponding on-shell distribution functions $f$, providing an extension to
the standard quantum Boltzmann equation.
  We have considered a number of applications to demonstrate the use of our
formalism, including the Klein problem, quantum reflection from a CP-violating
mass wall and coherent production of (fermionic and scalar) particles in an
oscillating background. Our formalism should be of relevance for many problems
in particle physics and cosmology, including baryogenesis and neutrino flavour
oscillations in an inhomogeneous background.
