Object-relative ultraviolet weighting of electromagnetic modes and one-loop ultraviolet finiteness of internal photon lines in quantum electrodynamics
Abstract
This work explores whether localized electromagnetic interactions can be modeled by a physically concluded object-relative ultraviolet weighting of photon modes. The proposal is motivated heuristically by a weak-field self-backreaction estimate for localized energy-carrying modes and by a three-dimensional overlap argument. In the resulting ansatz, the infrared sector remains unchanged up to a characteristic angular wavenumber k_c, while ultraviolet contributions are suppressed asymptotically by a factor of order k_c^3/k^3. The mode structure is object-relative: a real photon is weighted by its frequency u k in the rest frame of the interaction object with four-velocity u. The occupation of the modes and the amplitudes of the vacuum fluctuations, in contrast, follow the rules of special relativity, so that virtual photons in loops are weighted by the invariant k k, i.e. by the Euclidean photon momentum. The weighting applies to photon lines only; applied in the same way to the electron line, it conflicts with gauge invariance or with the measured running of the fine-structure constant. One-loop diagrams with internal photon lines become ultraviolet finite, and the weighting can be represented by a gauge-invariant kinetic term of the photon field, so that the Ward-Takahashi identities are preserved. Four test cases are discussed. A Bethe-type estimate of the Lamb shift places the characteristic scale near the electron Compton wavenumber. The anomalous magnetic moment and the relativistic part of the Lamb shift show, however, that a photon weighting at this scale requires additional structure on the electron line to remain compatible with high-precision measurements. This structure, the vacuum polarization, and the spectral consistency of the weighting define the tasks for future work.
Related
- Measurement of the relative phase between the strong and electromagnetic amplitudes in J/ψ→ Σ+ Σ̅−
- Green's functions and weighting fields for dielectric multilayer geometries
- Quasinormal modes of massive scalar perturbations in slow-rotation bumblebee black holes with traceless conformal electrodynamics
- Infrared Problem in Quantum Electrodynamics
- Hybrid Variational Quantum-Classical Framework with Adaptive Weighting and Efficiency Assessment
BibTeX
@misc{rembe2026objectrelative,
title = {{Object-relative ultraviolet weighting of electromagnetic modes and one-loop ultraviolet finiteness of internal photon lines in quantum electrodynamics}},
author = {Christian Rembe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.16096},
eprint = {2607.16096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16096},
}
RIS
TY - UNPB
TI - Object-relative ultraviolet weighting of electromagnetic modes and one-loop ultraviolet finiteness of internal photon lines in quantum electrodynamics
AU - Christian Rembe
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2607.16096
UR - https://arxiv.org/abs/2607.16096
AB - This work explores whether localized electromagnetic interactions can be modeled by a physically concluded object-relative ultraviolet weighting of photon modes. The proposal is motivated heuristically by a weak-field self-backreaction estimate for localized energy-carrying modes and by a three-dimensional overlap argument. In the resulting ansatz, the infrared sector remains unchanged up to a characteristic angular wavenumber k_c, while ultraviolet contributions are suppressed asymptotically by a factor of order k_c^3/k^3. The mode structure is object-relative: a real photon is weighted by its frequency u k in the rest frame of the interaction object with four-velocity u. The occupation of the modes and the amplitudes of the vacuum fluctuations, in contrast, follow the rules of special relativity, so that virtual photons in loops are weighted by the invariant k k, i.e. by the Euclidean photon momentum. The weighting applies to photon lines only; applied in the same way to the electron line, it conflicts with gauge invariance or with the measured running of the fine-structure constant. One-loop diagrams with internal photon lines become ultraviolet finite, and the weighting can be represented by a gauge-invariant kinetic term of the photon field, so that the Ward-Takahashi identities are preserved. Four test cases are discussed. A Bethe-type estimate of the Lamb shift places the characteristic scale near the electron Compton wavenumber. The anomalous magnetic moment and the relativistic part of the Lamb shift show, however, that a photon weighting at this scale requires additional structure on the electron line to remain compatible with high-precision measurements. This structure, the vacuum polarization, and the spectral consistency of the weighting define the tasks for future work.
ER -