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.

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to hold for large values of A. . We have checked explicitly the agreement of the free energy of the standard and reduced models in lower orders of perturbation theory in arbitrary dimensions I up to (1/A)']. It is extremely important to check if the equivalence of the models persists at small values of A. . We are grateful to Professor E. Brdzin for his critical remark on the original version of our manuscript. Note added. -After the submission of this paper we received a preprint by G. Bhanot, U. Heller, and H. Neuberger where some evidence for a spontaneous breakdown of U(1) symmetry a.t small A. is presented. We understand that M. Peskin and K. Wilson have obtained similar results.K. Wilson, Phys. Rev. D 10, 2445(1974; J. Kogut -and L. Susskind, Phys. Bev. D 11, 395 (1975). E. Witten, Cargese Lecture Notes, 1979 (unpublished); Pu. M. Makeenko and A. A. Migdal, Phys. Lett. 88B, 135 (1979).

In high energy heavy ion collisions at the Relativistic Heavy Ion Collider ͑RHIC͒ at Brookhaven and the Large Hadron Collider at CERN, each central event will contain multiple pairs of heavy quarks. If a region of deconfined quarks and gluons is formed, a mechanism for additional formation of heavy quarkonium bound states will be activated. This is a result of the mobility of heavy quarks in the deconfined region, such that bound states can be formed from a quark and an antiquark that were originally produced in separate incoherent interactions. Model estimates of this effect for J/ production at RHIC indicate that significant enhancements are to be expected. Experimental observation of such enhanced production would provide evidence for deconfinement unlikely to be compatible with competing scenarios.

We study the phase-space correlation function for the Dirac vacuum in the presence of simple field configurations. Our formalism rests on the Wigner transform of the Dirac-Heisenberg correlation function of the Dirac field coupled to the electromagnetic field. A self-consistent set of equations obeyed by the 16 components of the phase-space correlation function and by the electric and magnetic field is derived. Our approach is manifestly gauge invariant. A closed system of integro-differential equations is obtained neglecting the quantum fluctuations of the electromagnetic field as should be appropriate for strong fields. These equations are an extension of the Vlasov equations used in the description of plasma. Our first applications address the production of particles in strong external fields. We set a framework for the inclusion of the back reaction of produced particles and for the description of the local changes of the vacuum state. I. I N T R O D U C T I O NThe structure of the QCD vacuum has been considered an important element for the understanding of stronginteraction physics [I]. T h e electroweak vacuum I-Iiggs field is believed to be the origin of all elementary-particle masses [2]. T h e QED vacuuln in strong fields has been explored both theoretically and experimentally in heavyion collisions and there is a significant discrepancy between the observed particle spectra and the theoretical predictions [3]. All this calls for a renewed effort to develop a systematic framework to describe the structure of the vacuum in a manner which would be to a large degree independent of perturbative quantum field theory. Despite its historical name, the vacuum state is not empty; it is populated with myriads of virtual particles which endow it with a rich structure. The standard, perturbative formulation of quantum field theory deeinphasizes this fact by treating the vacuum as just the simplest possible reference state: the one with the lowest possible energy and with all the relevant symmetry properties. All the remaining state vectors that are introduced to model real physical situations are defined relative to this unique reference state by building excitations on top of the ground state. This pragmatic approach enables one to calculate effectively the elements of the S matrix with the help of appropriate Feynman diagrams without ever paying attention to the problem of the internal structure of the vacuum and to its time evolution.In our opinion, in order to obtain an effective description of the local vacuum structure and its time evolution, we should use a single time parameter. This will enable us to treat the &ED vacuum as a genuine dynamical system with its fully prescribed dynamics, its conservation laws, and a whole new category of physical phenomena that take place in the phase space of virtual particles. There is an obvious drawback that the correlation functions will not be manifestly covariant, although the theory will remain relativistically in-variant. On the other hand, we will gain by introducin...