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PreprintCC BY 4.0arXiv

Detector Resolution and Observable Infrared Memory in QED

  • Takeshi Fukuyama
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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 ωmax, 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 ωmax are not observed and are effectively traced over. The corresponding soft-sector overlap therefore becomes resolution dependent, Dij=Dij(ωmax). 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.

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Cite

BibTeXRIS
BibTeX
@misc{fukuyama2026detector,
  title = {{Detector Resolution and Observable Infrared Memory in QED}},
  author = {Takeshi Fukuyama},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2606.08879},
  eprint = {2606.08879},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.08879},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Detector Resolution and Observable Infrared Memory in QED
AU  - Takeshi Fukuyama
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2606.08879
UR  - https://arxiv.org/abs/2606.08879
AB  - 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.
ER  -