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Scattering in 3+1-dimensional QED is believed to give rise to transitionsbetween different photon vacua. We show that these transitions can be removedby taking into account off-shell modes which correspond to Li\'enard-Wiechertfields of asymptotic states. This makes it possible to formulate scattering in3+1-dimensional QED on a Hilbert space which furnishes a single representationof the canonical commutation relations (CCR). Different QED selection sectorscorrespond to inequivalent representations of the photon CCR and are stableunder the action of an IR finite, unitary S-matrix. Infrared divergences arecancelled by IR radiation. Using this formalism, we discuss the time-dependenceof decoherence and phases of out-going density matrix elements in the presenceof classical currents. The results demonstrate that although no informationabout a scattering process is stored in strictly zero-energy modes of thephoton field, entanglement between charged matter and low energy modesincreases over time.

Infrared-safe scattering without photon vacuum transitions and time-dependent decoherence