Object-relative ultraviolet weighting of electromagnetic modes and one-loop ultraviolet finiteness in quantum electrodynamics

Abstract

This work explores whether localized electromagnetic interactions can be modeled in terms of an effective object-relative ultraviolet weighting of internal modes. The proposal is motivated heuristically by two considerations: a weak-field self-backreaction estimate for sufficiently localized energy-carrying modes and a three-dimensional overlap argument for localized interactions. In the resulting ansatz, the infrared sector remains unchanged up to a characteristic scale the at angular wavenumber $k_c$, while ultraviolet contributions are suppressed asymptotically by a factor of order $k_c^3/k^3$ with the angular wavenumber $k$. Because a crossover based solely on $k^μk_μ$ is not well suited to the intended mode-based interpretation, the weighting is formulated in terms of the object-relative covariant mode variable $u_μ k^μ$ with the four-velocity $u^μ$, i.e. the mode frequency measured in the rest frame of the localized interaction object. Within this restricted framework, selected one-loop QED contributions considered here become ultraviolet finite, and a restricted one-loop Ward-consistency check is preserved when the same scalar weighting is assigned consistently to the same internal photon mode in self-energy and vertex corrections. Four initial test cases are discussed: the anomalous magnetic moment, a Bethe-type low-energy Lamb-shift estimate, the Casimir effect, and a compact ultraviolet one-loop test. In the first three cases, the weighting leads to physically sensible characteristic scales associated with the electron Compton scale, an atomic bound-state scale, and plate distance, respectively. The results suggest that different observables may probe different effective localization scales. Action-level derivation, spectral consistency, and extension beyond one loop remain open problems.