Detector Resolution and Observable Infrared Memory in QED
AIPR assessment
Problem difficulty: this sits in an active and fairly saturated theoretical area, with many groups working on infrared structure, dressing, memory, and asymptotic symmetries. Strengths reinforce each other in a light but real way, the argument is simple, the bridge across subtopics is elegant, and the formulas are standard enough to make the message credible. The weaknesses also reinforce each other, because the paper is largely interpretive, lacks an independent example or quantitative check, a
Abstract
Infrared divergences in QED cancel in inclusive observables through the Bloch--Nordsieck and KLN mechanisms. However, this cancellation removes only the unphysical infrared regulator. The detector resolution scale $ω_{\max}$, which specifies the maximum energy of unresolved soft photons, remains in the observable cross section. We emphasize that this surviving scale has a natural interpretation as a coarse-graining scale in the reduced density matrix of the hard sector. Soft photons below $ω_{\max}$ are not observed and are effectively traced over. The corresponding soft-sector overlap therefore becomes resolution dependent, $D_{ij}=D_{ij}(ω_{\max})$. Observable infrared memory is consequently defined not only by the asymptotic soft sector itself, but also by the resolution scale separating observed and unobserved infrared degrees of freedom. This provides a bridge between the traditional infrared-safe cross-section formulation and the modern interpretation of soft photons as carriers of infrared memory and quantum information.