Infrared Divergences and Quantum Coherence

TL;DR

This paper explores how infrared divergences in theories with long-range forces affect quantum coherence, proposing a method to preserve some coherence in IR-finite density matrices based on unitarity.

Contribution

It introduces a way to define IR-finite density matrices that retain partial quantum coherence, challenging the notion of complete decoherence due to IR effects.

Findings

IR-finite density matrices can preserve some quantum coherence

Loss of coherence depends on scattering kinematics

Proposes a unitarity-based approach to IR divergences

Abstract

In theories with long-range forces like QED or perturbative gravity, only rates that include emitted soft radiation are non-vanishing. Independently of detector resolution, finite observables can only be obtained after integrating over the IR-component of this radiation. This integration can lead to some loss of quantum coherence. In this note, however, we argue that it should in general not lead to full decoherence. Based on unitarity, we suggest a way to define non-vanishing off-diagonal pieces of the IR-finite density matrix. For this IR-finite density matrix, we estimate the dependence of the loss of quantum coherence, i.e. of its purity, on the scattering kinematics.