QED scattering amplitudes in the Fock basis are infrared divergent — soft virtual photons contribute infinite corrections that must be cancelled against soft real emission. The Faddeev-Kulish approach dresses incoming and outgoing charged particles with coherent clouds of soft photons below an energy scale E_d, removing the divergences order by order in perturbation theory.
This paper works out the explicit dressed amplitudes for specific processes, displaying how the soft factors depend on the hard particles' momenta and total angular momenta. The dressings effectively regulate virtual soft photon contributions at the scale E_d, making the Faddeev-Kulish hard amplitudes equivalent to the infrared-finite part of standard Fock-basis amplitudes.
The key result concerns subleading soft dressings. When the photon clouds are extended beyond leading order in the soft-momentum expansion, tree-level soft-photon emission is suppressed. The dressing doesn't just cancel divergences — at subleading order, it actively reduces the emission of additional soft radiation. The charged particle's coherent photon cloud absorbs what would have been emitted. The infrared cure doesn't merely regulate the pathology; it changes the physical prediction for soft radiation in a direction that makes the dressed states more silent.