Reduced-action-integral approach for photon-photon interactions in vacuum
Phys. Rev. A 113, 033732 – Published 31 March, 2026
DOI: https://doi.org/10.1103/ghy3-1ttg
Abstract
Electromagnetic waves propagating through vacuum can polarize virtual electron-positron pairs; this polarization in turn nonlinearly modifies their propagation. A semiclassical nonlinear wave equation describing the propagation is derived from the Euler-Heisenberg Lagrangian density, which captures vacuum polarization effects up to the one-loop level. Here we present a reduced-action-integral approach that enables rapid modeling of nonlinear phenomena arising from the Euler-Heisenberg Lagrangian. Application of the variational principle to the reduced action provides equations of motion for familiar light-pulse parameters, such as spot size, phase, polarization, and phase-front curvature, without requiring full-field simulations. Three examples demonstrate the utility of the approach: phase modulation, birefringence, and frequency mixing.
