Corrected Calculation for the Non-local Solution to the g-2 Anomaly and Novel Results in Non-local QED

TL;DR

This paper corrects previous calculations of the muon g-2 in non-local QED, introduces new computational techniques, and explores implications for charge quantization and bounds on non-locality scale, with various novel results in non-local QED.

Contribution

It provides a corrected method for loop calculations in non-local QED and presents new results on photon self-energy, Coulomb potential, hydrogen energy levels, and Lamb shift in this framework.

Findings

Corrected muon g-2 calculation in non-local QED

Derived bounds on non-locality scale from neutrino charge constraints

Identified the need for renormalization in non-local QFTs

Abstract

We provide the corrected calculation of the muon g-2 in non-local QED previously done in the literature. In specific, we show the proper technique for calculating loops in non-local QED and use it to find the form factors F1(q1) and F2(q2) in non-local QED. We also utilize this technique to calculate some novel results in non-local QED, including calculating the correction to the photon self-energy, the modification to the classical Coulomb potential, the modification to the energy levels of the hydrogen atom, and the contribution to the Lamb shift. We also discuss charge dequantization through non-locality, and show that the experimental bounds on the electric charge on Dirac neutrinos, translate into strong flavor-dependent bounds on the scale on non-locality that range between 10^5 - 10^10 TeV. We also discuss the inconsistencies of unrenormalized non-local Quantum Field Theories (QFTs) and the need for renormalizing them, even when they are free from UV divergences.