Abstract
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\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g-2$$\\end{document} anomalies.
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