  We study the Bogoliubov-Dirac-Fock model which is a mean-field approximation
of QED. It allows to consider relativistic electrons interacting with the Dirac
sea. We study the system of two electrons in the vacuum: it has been shown in a
previous work that an electron alone can bind due to the vacuum polarization,
under some technical assumptions. Here we prove the absence of binding for the
system of two electrons: the response of the vacuum is not sufficient to
counterbalance the repulsion of the electrons.
