Phenomenological implications of nonlocal quantum electrodynamics

We analyze several phenomenological implications of a nonlocal generalization of quantum electrodynamics (QED). We compute the nonlocal corrections to the photon propagator up to one loop, and we show that nonlocality leads to a change of the Coulomb potential. We then investigate the ensuing modifications to the Lamb shift and to the electrostatic forces and comparing our results with the data from the muonic hydrogen anomaly, we set lower bounds on the nonlocality scales. We also discuss the running of the electromagnetic coupling for the nonlocal theory. The results obtained indicate that future experimental analyses on atomic phenomena, such as the Lamb shift, could allow to verify the presence of non-local effects on microscopic scales and impose effective limits on the non-locality scale.