Photon pairing and the strong coupling phase of massive quantum electrodynamics Cooper equation

In this paper, through the Cooper equation of the photon pairing, the instability of the normal vacuum of the Quantum Electrodynamics with the massive electron is studied. Using the low energy effective Lagrangian, the normal vacuum is shown to be unstable against the condensation of the photon pairs above the critical value of the fine structure constant. These agree with the previous results obtained by the Bethe-Salpeter equation. The presence of the weak electric external field enhances the instability thus lowering the critical value. This can be a basis for the explanation of the anomalous GSI e+e- events