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

TL;DR

This paper presents a new formulation of 3+1-dimensional QED scattering that eliminates photon vacuum transitions by including off-shell modes, leading to IR-finite, stable scattering sectors and insights into decoherence and entanglement dynamics.

Contribution

It introduces a formalism incorporating off-shell modes to remove photon vacuum transitions, enabling IR-finite scattering with a single CCR representation.

Findings

Photon vacuum transitions can be removed with off-shell modes.

Infrared divergences are canceled by IR radiation.

Entanglement between matter and low-energy modes increases over time.

Abstract

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.