Vacuum polarization in a one-dimensional effective quantum-electrodynamics model
Abstract
With the aim of progressing toward a practical implementation of an effective quantum-electrodynamics (QED) theory of atoms and molecules, which includes the effects of vacuum polarization through the creation of virtual electron-positron pairs but without the explicit photon degrees of freedom, we study a one-dimensional effective QED model of the hydrogen-like atom with delta-potential interactions. This model resembles the three-dimensional effective QED theory with Coulomb interactions while being substantially simpler. We provide some mathematical details about the definition of this model, calculate the vacuum-polarization density, and the Lamb-type shift of the bound-state energy, correcting and extending results of previous works. We also study the approximation of the model in a finite plane-wave basis, and in particular we discuss the basis convergence of the bound-state energy and eigenfunction, of the vacuum-polarization density, and of the Lamb-type shift of the bound-state energy. We highlight the difficulty of converging the vacuum-polarization density in a finite basis and we propose a way to improve it. The present work could give hints on how to perform similar calculations for the three-dimensional effective QED theory of atoms and molecules.
Cite
@article{arxiv.2411.07246,
title = {Vacuum polarization in a one-dimensional effective quantum-electrodynamics model},
author = {Timothée Audinet and Umberto Morellini and Antoine Levitt and Julien Toulouse},
journal= {arXiv preprint arXiv:2411.07246},
year = {2025}
}