Based on order one-loop effective Lagrangian derived from the 2-point photon vertex in quantum electrodynamics, we obtain a quantum modified Maxwell equations, and the classical expression of retarded potential is consequently modified by these equations. The results indicate that, due to the time-space non-locality of vacuum polarization, the vacuum polarization current is delayed relative to the field variation and induces a series of additional retarded potentials except for the classical part of retarded potential. Particularly, compared to the classical potential, these additional potentials are further retarded. Because the retard potential is the base of theory of electromagnetic radiation, the results of this work are of great value to the studies of quantum effect in ultra-intense electromagnetic radiation.
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