  Quantum electrodynamics is generally extended to a nonlocal QED by
introducing the correlation functions. The gauge link is introduced to
guarantee that the nonlocal QED is locally U(1) gauge invariant. The
corresponding Feynman rules as well as the proof of Ward-Takahashi identity are
presented. As an example, the anomalous magnetic moments of leptons are studied
in nonlocal QED. At one-loop level, besides the ordinary diagrams, there are
many additional Feynman diagrams which are generated from the gauge link. It
shows the nonlocal QED can provide a reasonable explanation for lepton g-2
anomalies.
