Self-consistent Approach to Off-Shell Transport

The properties of two forms of the gradient expanded Kadanoff--Baym equations, i.e. the Kadanoff--Baym and Botermans-Malfliet forms, suitable to describe the transport dynamics of particles and resonances with broad spectral widths, are discussed in context of conservation laws, the definition of a kinetic entropy and the possibility of numerical realization. Recent results on exact conservations of charge and energy-momentum within Kadanoff-Baym form of quantum kinetics based on local coupling schemes are extended to two cases relevant in many applications. These concern the interaction via a finite range potential, and, relevant in nuclear and hadron physics, e.g. for the pion--nucleon interaction, the case of derivative coupling.