Abstract
The mathematical properties of the solutions of the Dirac equation in over-critical external potentials are investigated. The 1/r Coulomb potential is treated as the limitR → 0 of cut-off Coulomb potentials (R is the cut-off parameter). The results are interpreted in terms of quantum electrodynamics. A number of new physical phenomena occur in quantum electrodynamics of strong fields. One of the most interesting ones is the autoionization of positrons (energyless creation of electron-positron pairs) in over-critical external fields.
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