An Analytic Form for the Effective Lagrangian of QED and its Application to Pair Production and Photon Splitting

TL;DR

This paper derives an analytic expression for the Heisenberg-Euler Lagrangian in QED, enabling estimates of pair production and photon splitting rates in strong electromagnetic fields, advancing theoretical understanding of quantum electrodynamics phenomena.

Contribution

It provides an all-orders analytic form of the effective Lagrangian for weak and strong fields, facilitating precise calculations of pair production and photon splitting rates.

Findings

Analytic expressions for the effective Lagrangian in various field regimes

Estimates of pair-production rates in strong electric fields

Estimates of photon-splitting rates in strong magnetic fields

Abstract

We derive an analytic form for the Heisenberg-Euler Lagrangian in the limit where the component of the electric field parallel to the magnetic field is small. We expand these analytic functions to all orders in the field strength ($F_{\mu\nu}F^{\mu\nu}$) in the limits of weak and strong fields, and use these functions to estimate the pair-production rate in arbitrarily strong electric fields and the photon-splitting rate in arbitrarily strong magnetic fields.