A Reduced Action Integral for Photon-Photon Interactions in Vacuum

TL;DR

This paper introduces a simplified variational approach based on a reduced action integral to efficiently model nonlinear vacuum polarization effects on light propagation, enabling quick analysis of phenomena like phase modulation and birefringence.

Contribution

A novel reduced-action-integral method derived from the Euler--Heisenberg Lagrangian for rapid modeling of photon-photon interaction effects in vacuum.

Findings

Efficient equations of motion for light pulse parameters derived

Demonstrated modeling of phase modulation, birefringence, and frequency mixing

Validated approach with three example applications

Abstract

Electromagnetic waves propagating through vacuum can polarize virtual electron-positron pairs; this polarization, in turn, nonlinearly modifies their propagation. A semi-classical 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.