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

@article{Gravejat2009GroundSA,
  title={Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms},
  author={P. Gravejat and M. Lewin and {\'E}. S{\'e}r{\'e}},
  journal={Communications in Mathematical Physics},
  year={2009},
  volume={286},
  pages={179-215}
}
  • P. Gravejat, M. Lewin, É. Séré
  • Published 2009
  • Physics, Mathematics
  • Communications in Mathematical Physics
  • 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 as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of… CONTINUE READING

    Figures from this paper.

    Existence of ground state of an electron in the BDF approximation
    5
    Renormalization of Dirac ’ s Polarized Vacuum Mathieu Lewin
    Renormalization and Asymptotic Expansion of Dirac’s Polarized Vacuum
    14
    Charge renormalisation in a mean-field approximation of QED
    3
    Charge Renormalization and Static Electron/Positron Pair Production for a Nonlinear Dirac Model with Weak Interactions
    4
    Derivation of the magnetic Euler-Heisenberg energy
    5
    Large quantum systems: a mathematical and numerical perspective
    4

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 38 REFERENCES
    Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics
    44
    The Mean-Field Approximation in Quantum Electrodynamics. The no-photon case
    57
    Existence of a Stable Polarized Vacuum in the Bogoliubov-Dirac-Fock Approximation
    77
    SELF-CONSISTENT SOLUTION FOR THE POLARIZED VACUUM IN A NO-PHOTON QED MODEL
    49
    Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics
    63
    The quantum theory of the electron
    2032
    A theory of electrons and protons
    349
    A New Approach to the Modeling of Local Defects in Crystals: The Reduced Hartree-Fock Case
    78