Quantum Electrodynamics of Strong Fields

Abstract

Quantum electrodynamics of strong external fields is investigated in the context of atomic physics. If the electromagnetic coupling constant Z a becomes sufficiently large (Z > l / a % 137 for point sources or Z > 172 for extended nuclei) bound electron states can join the negative-energy continuum of the Dirac equation. The resulting possibility of spontaneous positron production and the new concept of a charged electron-positron vacuum is discussed under several aspects. The autoionization model and the exact overcritical solutions of the single-particle Dirac equation are contrasted with a quantum-field-theoretical approach. Non-linear field effects are shown to have no influence. Vacuum polarization and the self-screening of extremely strong electric charges are treated explicitly. Adiabatic collisions of heavy ions leading to the transient formation of quasimolecular electron orbitals are suggested as a means for an experimental test of the special features of strong-field QED, After an introduction to the relativistic two-centre Dirac equation, the x-ray spectroscopy of quasimolecules and the spontaneous and induced positron emission in, for example, U-U collisions are discussed. The importance of several background processes is stressed. Finally, strong-field aspects for nuclear matter and in gravitation are mentioned.

Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields

“…In our language, the Pauli-Villars method consists in introducing the following energy functional It is well-known in the Physics literature [32,20,3] that only two auxiliary fields are necessary to fulfill these conditions, hence we shall take J = 2 in the rest of the paper. In this case, the condition (2.12) is equivalent to…”

“…(iv) The functional F 2 is the non-negative and bounded quadratic form on L 2 (R 3 , R 4 ) given by 20) where…”

“…The function M describes the linear response of the Dirac sea. It is wellknown in the Physics literature [20,Eq. (5.39)].…”

“…In this model the interaction between the Dirac particles is mediated by the classical electromagnetic field which accounts for photons. This approach to vacuum polarization is usual in the Physics literature (see, e.g., [36,20]). …”

“…In a celebrated paper, Schwinger [36] used (1.3) (and a time-dependent version of it) to derive the probability of pair creation by tunneling in a strong electrostatic field. For more recent works on the subject, see the references in [20]. Several ongoing experiments aim at detecting some nonlinear effects of the vacuum in the laboratory [6].…”