The standard layman description of QED is that forces are no longer mediated by fields present at all points in space, but by particles that are (presumably?) at least somewhat localized, and carry some energy. Forces are then exchanged between two electrons by "exchanging photons" -- at the most basic level, it's usually at least implied that this works like momentum transferred between two people passing a ball back and forth, but there's usually a disclaimer that this "isn't exactly right". However, the examples given inevitably deal with the very specific phenomena of radiation emission -- where classically energy is lost by the emitter (electron) and carried away by the field...if static fields are mentioned, they are quickly dismissed with a mention of "virtual photons". So, my question: what is the QED explanation for the Coulomb force between two particles constrained to sit motionless in proximity of one another? E.g. Does modern understanding of QED really add anything to the description of the forces beyond classical one of force-carrying fields?