This Advanced Study Institute (ASI) brought together two distinct ·"schools of approach" to Quantum Electrodynamics (QED) in the presence of intense, external, electromagnetic fields, in an effort to lay a joint foundation for a needed theoretical explanation of the sharp e+ e- "resonances" observed in the scattering of very heavy IOns. These (GSI/Darmstadt) experiments, whose history, latest reconfirmations, and most recent data were presented in three opening sessions (Bokemeyer, Koenig), show a smooth background of positron (e+) production, as a function of e+ kinetic energy. Superimposed upon this background are four very sharp peaks, of narrow widths (~ 30 KeV) and of clear experimental significance ('" 5 standard deviations). Most ofthese peaks correspond to sharp, essentially back-to-back electron-positron emission in the ions' center of mass. Following the approach of "supercritical" potential theory (SPT), where the total ionic charge unit Z satisfies Z > 137, it has been possible to provide a detailed and apparently correct understanding of the smooth e+ e- background; a coherent description of different facets of this approach, emphasizing the nature of the charged, supercritical vacuum, was described by the authors responsible for the invention of SPT (Greiner, Muller, Rafelski). In addition, predictions for related phenomena were outlined by other lecturers using the SPT approach (Bawin, Soff, SsJrensen).

Introductory Remarks.- Vacuum Structure - An Essay.- Investigation of (e+e?) Correlations in Heavy Ion Collisions with the Double ORANGE Spectrometer.- Positron Line Emission in Very Heavy Ion Collisions: Results from the EPOS Collaboration.- Particles in Strong/Supercritical Fields.- Strong Coulomb Coupling of Charged Particles.- Quantum Electrodynamical Corrections in Critical Fields.- Channeling, Bremsstrahlung and Pair Creation in Single Crystals.- QED in Strong Coulomb Fields: Charged Vacuum, Atomic Clock, and Correlated, Narrow e+e? - Lines.- Production of Hypothetical X0-Mesons in High-Energy Channeling Reactions.- Pair Conversion in Sub- and Supercritical Potentials.- Production of Exotic Particles in Ultrarelativistic Heavy-Ion Collisions.- Quantum Electrodynamics in Intense Fields.- Application of the Proper-Time Method to Non-Perturbative Effects in QED.- A New Phase of QED in Strong Coupling: A Guide for the Perplexed.- Continuum Limit of Quenched QED. Critical Exponents and Anomalous Dimensions.- Non-Perturbative External Field Effects in QED.- Functional Integrals in the Strong Coupling Regime.- A Phase Transition of QED, Schwinger's Proper Time Formalism; Chemical Potential and Electric Field.- Are There Background Fields That Can Induce QED Phase Transitions at Weak Coupling?.- New QED, the GSI Peaks, and Background Fields.- Functional Approach to Strong-Coupling in (QED)4 and (QCD)4.- Related Quantum Field Theory/Particle Theory Considerations.- The Gluon Anomaly in the Proton Spin.- Lectures on Solitons.- Renormalization Group and Stability Analysis of ??4 Theories.- Bosonization and Its Application to Nonperturbative Phenomena in Field Theories.- Remarks on Cosmic Strings, Aharonov-Bohm Effect and Vacuum Polarization.- On Power Correctionsin Finite Temperature QCD.- Vacuum Structure in QCD.- Quantum Vacuum, Confinement and Acceleration.- The (First) Three B's of the Skyrme Model.- Pair Production in an Electric Field in a Time-Dependent Gauge: A Treatment Parallel to the Cosmological Particle Production.- Zero-Point Field in Non-Inertial or Confined Systems (Physically Measurable Manifestations of Vacuum).- Symplectic and Large-N Gauge Theories.- Summary Lecture.- Summary Lecture: Vacuum Structure in Intense Fields.