Is there a "zeroth-order" effect in quantum field theory (QED) that two electrons move from two fixed spacetime points to two other fixed spacetime points without the presence of virtual photons? Of course these spacetime points must be "fairly close" because when they are far apart then it seems obvious that the electrons don't feel eachother's presence so no photons are involved but the electrons travel instead independently from their initial points to their final points in all possible ways. But it their initial points and final points are not too far separated in space is there a zeroth order feynman diagram, i.e., two disconnected lines (representing all possible non-interacting paths)?
This question appears to be based on the interpretation of internal Feynman propagators as particles. However, the graphs are representations of terms of a perturbation expansion and only the external legs are particles. Therefore the question actually means, are there cases where the Coulomb interaction between two electrons can be ignored. Of course there are, if the electrons are far enough apart at their closest encounter.
In conclusion and to be clear, there is zero probability that two electrons do not interact. However if they are are far enough apart, their interaction may be neglected.