Maxwell equation with quantum corrections for vacuum in strong laser field

Modern lasers are yet unable to cause electron-positron pair production in vacuum, however it is possible to notice considerable influence of vacuum polarization on radiation that propagates in such medium. The field strength of modern lasers is not strong enough for creation of electron-positron pair in a vacuum, but the powerful laser beams generates polarization of vacuum which can be established experimentally. In the framework of QED a nonlocal theory of interaction of intensive laser radiation with electron-positron vacuum is developed. Refusing from the Heisenberg-Euler approximation it appears to be possible to calculate non-zero response of vacuum even for a plane wave. It is described by corrections to the Maxwell equations obtained by means of the proper time method. Effects generated by this correction for propagation of wave are analyzed.