Positronium collapse in hypercritical magnetic field and restructuring of the vacuum in QED

Abstract

\\The Bethe-Salpeter equation in a strong magnetic field is studied for positronium atom in an ultra-relativistic regime, and a (hypercritical) value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state. The compensation becomes possible owing to the falling to the center phenomenon. The relativistic form in two-dimensional Minkowsky space is derived for the four-dimensional Bethe-Salpeter equation in the limit of an infinitely strong magnetic field, and used for finding the above hypercritical value. Once the positronium rest mass is compensated by the mass defect the energy barrier separating the electron-positron system from the vacuum disappears. We thus describe the structure of the vacuum in terms of strongly localized states of tightly mutually bound (or confined) pairs. Their delocalization for still higher magnetic field, capable of screening its further growth, is discussed.