The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

@article{Sok2014ThePA,
  title={The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics},
  author={J'er'emy Sok},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={57},
  pages={022304}
}
  • J'er'emy Sok
  • Published 7 July 2014
  • Physics
  • Journal of Mathematical Physics
The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence of the para-positronium, the bound state of an electron and a positron with antiparallel spins, in the BDF model represented by a critical point of the energy functional in the absence of an external… 
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References

SHOWING 1-10 OF 22 REFERENCES

The positronium in a mean-field approximation of quantum electrodynamics.

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon, mean-field approxi- mation of quantum electrodynamics. It describes relativistic electrons in the Dirac sea. In this model, a state is fully

Existence of ground state of an electron in the BDF approximation

The Bogoliubov–Dirac–Fock (BDF) model allows us to describe relativistic electrons interacting with the Dirac sea. It can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where

Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics

The Bogoliubov–Dirac–Fock (BDF) model is the mean-field approximation of no-photon quantum electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional

Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen

Existence of a Stable Polarized Vacuum in the Bogoliubov-Dirac-Fock Approximation

According to Dirac’s ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator D0. In the presence of an

Renormalization of the Regularized Relativistic Electron-Positron Field

Abstract: We consider the relativistic electron-positron field interacting with itself via the Coulomb potential defined with the physically motivated, positive, density-density quartic interaction.

Charge renormalisation in a mean-field approximation of QED

We study the Bogoliubov-Dirac-Fock (BDF) model, a no-photon, mean-field approxi- mation of quantum electrodynamics that allows to study relativistic electrons interacting with the vacuum. It is a

From quantum electrodynamics to mean-field theory. I. The Bogoliubov-Dirac-Fock formalism

A relativistic mean-field theory for interacting Dirac particles in an external field is derived from quantum-field theory using a minimisation principle, and discussed in the context of atomic

On the Stability of the Relativistic Electron-Positron Field

Abstract:We study the energy of relativistic electrons and positrons interacting through the second quantized Coulomb interaction and a self-generated magnetic field. As states we allow generalized

SELF-CONSISTENT SOLUTION FOR THE POLARIZED VACUUM IN A NO-PHOTON QED MODEL

We study the Bogoliubov–Dirac–Fock model introduced by Chaix and Iracane (1989 J. Phys. B: At. Mol. Opt. Phys. 22 3791–814) which is a mean-field theory deduced from no-photon QED. The associated