During a QFT class, my professor briefly explored the fact that infrared (IR) divergences can be removed from QED by considering "soft" photons that have an energy inferior to the detector sensitivity, arguing that such diagrams then cancel the IR divergence and make it unobservable. So in that example, we considered the IR divergence of the electron propagator, and added diagrams with one or more external photon(s).
This argumentation left me pretty unsatisfied, because we are adding there diagrams of a different kind (i.e. with external photon legs), and that means that if we had a perfect detector (such as nature has), the divergence would be observable if QED would be a perfect theory of nature.
I know we can remove the IR divergence by putting the system in a box, but I was wondering if there exists another way to remove IR divergences in continuous QFT (so no box)?