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Journal Articles The Journal of Chemical Physics Year : 2023

Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom

Abstract

We consider a one-dimensional effective quantum electrodynamics (QED) model of the relativistic hydrogen-like atom using delta-potential interactions. We discuss the general exact theory and the Hartree-Fock approximation. The present one-dimensional effective QED model shares the essential physical feature of the three-dimensional theory: the nuclear charge polarizes the vacuum state (creation of electron-positron pairs) which results in a QED Lamb-type shift of the bound-state energy. Yet, this 1D effective QED model eliminates some of the most serious technical difficulties of the three-dimensional theory coming from renormalization. We show how to calculate the vacuum-polarization density at zeroth order in the two-particle interaction and the QED Lamb-type shift of the bound-state energy at first order in the two-particle interaction. The present work may be considered as a step toward the development of a quantum-chemistry effective QED theory of atoms and molecules.
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Dates and versions

hal-04102685 , version 1 (22-05-2023)
hal-04102685 , version 2 (23-06-2023)

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Timothée Audinet, Julien Toulouse. Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom. The Journal of Chemical Physics, 2023, 158, pp.244108. ⟨10.1063/5.0152956⟩. ⟨hal-04102685v2⟩
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