A nonperturbative calculation of the electron's magnetic moment with truncation extended to two photons

TL;DR

This paper presents a nonperturbative calculation of the electron's magnetic moment in light-front QED using Pauli-Villars regularization, extending previous work to include two-photon states and achieving results consistent with experimental measurements.

Contribution

The study extends light-front QED calculations of the electron's magnetic moment to include two-photon Fock states, improving accuracy over single-photon models.

Findings

Agreement with experimental anomalous magnetic moment within numerical errors

Small systematic discrepancy likely due to missing electron-positron loops and three-photon effects

Demonstrates feasibility of nonperturbative light-front approach for QED calculations

Abstract

The Pauli--Villars (PV) regularization scheme is applied to a calculation of the dressed-electron state and its anomalous magnetic moment in light-front-quantized quantum electrodynamics (QED) in Feynman gauge. The regularization is provided by heavy, negative-metric fields added to the Lagrangian. The light-front QED Hamiltonian then leads to a well-defined eigenvalue problem for the dressed-electron state expressed as a Fock-state expansion. The Fock-state wave functions satisfy coupled integral equations that come from this eigenproblem. A finite system of equations is obtained by truncation to no more than two photons and no positrons; this extends earlier work that was limited to dressing by a single photon. Numerical techniques are applied to solve the coupled system and compute the anomalous moment, for which we obtain agreement with experiment, within numerical errors, but observe a small systematic discrepancy that should be due to the absence of electron-positron loops and of three-photon self-energy effects. We also discuss the prospects for application of the method to quantum chromodynamics.