Detector Resolution and Observable Infrared Memory in QED

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 ${\omega }_{\max }$, 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 ${\omega }_{\max }$ are not observed and are effectively traced over. The corresponding soft-sector overlap therefore becomes resolution dependent, $D_{ij}=D_{ij}({\omega }_{\max })$. 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.

Comments: 5 pages, no figure, The relation between detector-resolution flow, soft-photon coherence, electromagnetic memory, and infrared-safe dressed asymptotic states has been clarified, including the behavior of the properly dressed infrared limit. Relevant references have been added