Polarization of electron-positron vacuum by strong magnetic field in theory with fundamental mass

The exact Lagrangian function of the intensive constant magnetic field, replacing the Heisenberg-Euler Lagrangian in the traditional quantum electrodynamics, is calculated within the frames of the theory with the fundamental mass in the single-loop approximation. It is established that the obtained generalization of the Lagrangian function is substantial by arbitrary values of the magnetic field. The calculated Lagrangian in the weak field coincides with the known Heisenberg-Euler formula. The Lagrangian dependence on the field in the extremely strong fields completely disappears and it tends in this area to the threshold value, which is determined by the fundamental and lepton mass ratio