Solution of lepton $g-2$ anomalies with nonlocal QED

The explanation for lepton $g-2$ anomalies is provided with the nonlocal QED which is the simple extension of the standard model. This solution is based on the same gauge symmetry as QED without introducing any new particles and interactions. The correlation functions in the nonlocal strength tension and lepton-photon interaction make it possible to explain the discrepancies of both $\Delta a_\mu$ and $\Delta a_e$. With the same approach, the discrepancy of anomalous magnetic moment of $\tau$ lepton from standard model is estimated in the range $1.19\times10^{-5}$ to $3.21\times10^{-3}$ which is covered by the current experimental uncertainty.