A technique based on the Wigner distribution phase space interpretation of quantum mechanics is developed to obtain a transport theory capable of describing the high-field, inhomogeneous electronic transport in collision dominated sub-micron semiconductor devices. The problems associated with the general construction of quantum phase space distributions are considered using the Marcinkiewicz theorem which suggests that any defined quantum distribution which is both real and bounded must also, in general, be allowed to assume negative values. A pair of exact coupled transport equations for the one-electron and one-phonon Wigner distribution functions is obtained using multiple imaginary time Greens function techniques starting from a model Hamiltonian incorporating electron-electron and electron-phonon interactions as well as a coupling to externally applied space-and time-dependent electric and pressure fields. These exact equations exhibit a non-locality which may be interpreted in terms of the uncertainty relations of quantum mechanics. Assumptions are made (the many body correlation effects being approximated using functional derivative techniques) which restrict the resulting equations to the transition regime between the bulk scale device adequately modelled by Boltzmann transport and the microscopic region driven exclusively by boundary influences. These approximate equations maintain a non-locality due to the finite extent of a collision process thus allowing the collision integrals to become explicitly dependent on the driving field. Derived self-consistently within the collision integrals is a dynamical nonequilibrium screening of the interaction potentials which is also explicitly field-dependent. The field-dependence of the effective interactions is analysed for several model screening functions in two-and three-dimensional electron assemblies for a range of system parameters in GaAs. The results indicate that conventional screening overestimates the efficiency of the shielding process and that the action of a strong field within a collision event descreens the effective interaction potentials.