Letters in Mathematical Physics

, Volume 72, Issue 2, pp 99-113

First online:

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

  • Christian HainzlAffiliated withDepartment of Mathematics, University of Copenhagen
  • , Mathieu LewinandAffiliated withDepartment of Mathematics, University of Copenhagen
  • , Christof SparberAffiliated withDepartment of Numerical Mathematics, University of MünsterMünster Wolfgang Pauli Institute Vienna c/o Faculty of Mathematics, Vienna University Email author 

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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.


QED vacuum polarization Dirac equation HartreeFock model semilinear evolution equations.