Effects of Vacuum Polarization in Strong Magnetic Fields with an Allowance Made for the Anomalous Magnetic Moments of Particles

TL;DR

This paper derives a generalized Lagrangian for intense magnetic fields considering anomalous magnetic moments of electrons and positrons, revealing that in extremely strong fields, the Lagrangian becomes field-independent and is influenced solely by these moments.

Contribution

It provides an exact, real Lagrangian for strong magnetic fields in QED that accounts for anomalous magnetic moments, extending the Heisenberg-Euler framework.

Findings

Lagrangian matches Heisenberg-Euler in weak fields

Lagrangian becomes constant in extremely strong fields

Field dependence disappears at high intensities

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.