The Sharp Bound on the Stability¶of the Relativistic Electron-Positron Field¶in Hartree–Fock Approximation

Abstract:

It was shown in [2] that the energy of the relativistic electron-positron field interacting via a second quantized Coulomb potential in Hartree–Fock approximation is positive provided the fine structure constant is not bigger than 4/π. We show that it is instable if the fine structure constant is above this critical value. We do this partially by adapting an idea of Chaix, Iracane, and Lions [4] leading to an instability problem similar to the one of the no-pair hydrogen hamiltonian [5].