Absence of binding in a mean-field approximation of quantum electrodynamics

2014/07/07 by Jérémy Sok, Sok, Jérémy
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Cold Atom Physics and Bose-Einstein Condensates #Dirac (video compression format) #Dirac fermion #Dirac sea #Electron #FOS: Physical sciences #Fermion #Field (mathematics) #Fock space #Mathematical Physics (math-ph) #Mathematics #Physics #Polarization (electrochemistry) #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Spectral Theory in Mathematical Physics #Vacuum energy #Vacuum polarization #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1407.1600

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2014/07/07 · arxiv created 2014/09/15 · arxiv updated 2014/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Bogoliubov-Dirac-Fock model which is a mean-field approximation of QED. It allows to consider relativistic electrons interacting with the Dirac sea. We study the system of two electrons in the vacuum: it has been shown in a previous work that an electron alone can bind due to the vacuum polarization, under some technical assumptions. Here we prove the absence of binding for the system of two electrons: the response of the vacuum is not sufficient to counterbalance the repulsion of the electrons.

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

Related

• Charge renormalisation in a mean-field approximation of QED
• The positronium in a mean-field approximation of quantum electrodynamics
• The Mean-Field Approximation in Quantum Electrodynamics. The no-photon case
• A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics
• Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms