  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.
