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

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 Lienard-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.

Automated summary

The article discusses scattering in 3 + 1-dimensional QED and proposes a method to eliminate transitions between different photon vacua by considering off-shell modes. The results demonstrate an increase in entanglement between charged matter and low energy modes over time.