  We consider a small interacting sample coupled to several non-interacting
leads. Initially, the system is at thermal equilibrium. At some instant $t_0$
the system is set into the so called partition-free transport scenario by
turning on a bias on the leads. Using the theory of Volterra operators we
rigorously formulate a Dyson equation for the retarded Green's function and we
establish a closed formula for the associated proper interaction self-energy.
