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