Abstract
Given the anomalous magnetic moments of electrons and positrons in the one-loop approximation, we calculate the exact Lagrangian of an intense constant magnetic field that replaces the Heisenberg-Euler Lagrangian in traditional quantum electrodynamics (QED). We have established that the derived generalization of the Lagrangian is real for arbitrary magnetic fields. In a weak field, the calculated Lagrangian matches the standard Heisenberg-Euler formula. In extremely strong fields, the field dependence of the Lagrangian completely disappears and the Lagrangian tends to a constant determined by the anomalous magnetic moments of the particles.
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