A Novel Solution to the Klein-Gordon Equation in the Presence of a Strong Rotating Electric Field

TL;DR

This paper presents a new analytical solution to the Klein-Gordon equation under strong rotating electric fields, revealing significant deviations from traditional models and suggesting a need to revise existing QED cascade theories.

Contribution

A novel analytical solution to the Klein-Gordon equation in strong electric fields, highlighting conditions where standard wavefunctions are inadequate.

Findings

New solution differs significantly from Volkov wavefunction

Standard assumptions may lead to inaccuracies in QED cascade modeling

Conditions for solution validity are substantially different from previous estimates

Abstract

The Klein-Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the electromagnetic field amplitude. The condition for which the new solution recovers the familiar Volkov wavefunction naturally follows. When not satisfied, significant deviation from the Volkov wavefunction is demonstrated. The new condition is shown to differ by orders of magnitudes from the commonly used one. As this equation describes (neglecting spin effects) the emission processes and the particle motion in Quantum Electrodynamics (QED) cascades, our results suggest that the standard theoretical approach towards this phenomenon should be revised.