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

Abstract

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 physics. In this approach, electrons and positrons are treated on the same footing, and neither final 'reinterpretation' nor 'positive energy projection' are needed. The authors obtain mean-field equations of Dirac-Fock type containing a vacuum polarisation term that does not exist in the standard Dirac-Fock equations. However, the standard Dirac-Fock equations as well as the equations resulting from earlier attempts to build a mean-field theory from quantum electrodynamics, are recovered as non-variational approximations. The minimisation principle also leads to a new way of introducing finite-basis relativistic calculations.