Polarization of the Electron-Positron Vacuum by a Strong Magnetic Field in the Theory with a Fundamental Mass

In the framework of the theory with a fundamental mass in the one-loop approximation, we evaluate the exact Lagrange function of the strong constant magnetic field, replacing the Heisenberg–Euler Lagrangian in the traditional QED. We establish that the derived generalization of the Lagrange function is real for arbitrary values of the magnetic field. In the weak field, the evaluated Lagrangian coincides with the known Heisenberg–Euler formula. In extremely strong fields, the field dependence of the Lagrangian completely disappears; in this range, the Lagrangian tends to the limit value determined by the ratio of the fundamental and lepton masses.