Letters in Mathematical Physics

, Volume 72, Issue 2, pp 99–113

Existence of Global-In-Time Solutions to a Generalized Dirac-Fock Type Evolution Equation

  • Christian Hainzl
  • Mathieu Lewinand
  • Christof Sparber

DOI: 10.1007/s11005-005-4377-9

Cite this article as:
Hainzl, C., Lewinand, M. & Sparber, C. Lett Math Phys (2005) 72: 99. doi:10.1007/s11005-005-4377-9


We consider a generalized DiracFock type evolution equation deduced from nophoton Quantum Electrodynamics, which describes the selfconsistent timeevolution of relativistic electrons, the observable ones as well as those filling up the Dirac sea. This equation has been originally introduced by Dirac in 1934 in a simplified form. Since we work in a Hartree-Fock type approximation, the elements describing the physical state of the electrons are infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced by ChaixIracane (J. Phys. B., 22, 37913814, 1989), and recently established by Hainzl-Lewin-Séré, we prove the existence of globalintime solutions of the considered evolution equation.


QEDvacuum polarizationDirac equationHartreeFock modelsemilinear evolution equations.

Copyright information

© Springer 2005

Authors and Affiliations

  • Christian Hainzl
    • 1
  • Mathieu Lewinand
    • 1
  • Christof Sparber
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of CopenhagenCopenhagenDenmark
  2. 2.Department of Numerical MathematicsUniversity of Münster
  3. 3.Münster Wolfgang Pauli Institute Vienna c/o Faculty of MathematicsVienna UniversityViennaAustria