Due to coherence, there are strong electromagnetic fields of short duration in very peripheral collisions. They give rise to photon-photon and photon-nucleus collisions with a high flux up to an invariant mass region hitherto unexplored experimentally. After a general survey of the field equivalent photon numbers and photon-photon luminosities, especially for relativistic heavy ion collisions, are discussed. Special care needs to be taken to include the effects of the strong interaction and nuclear size in this case. Photon-photon and photon-hadron physics at various invariant mass scales are then discussed. The maximum equivalent photon energy in the lab-system (collider frame) are typically of the order of 3 GeV for RHIC and 100 GeV for LHC. Diffractive processes are an important background process. Lepton-pair, especially electron-positron pair production is copious. Due to the strong fields there will be new phenomena, like multiple e + e − pair production. The experimental techniques to select γγ-processes are finally discussed together with important background processes.

In central collisions at relativistic heavy ion colliders like the Relativistic Heavy Ion Collider RHIC/Brookhaven and the Large Hadron Collider LHC (in its heavy ion mode) at CERN/Geneva, one aims at detecting a new form of hadronic matter -the Quark Gluon Plasma. It is the purpose of this review to discuss a complementary aspect of these collisions, the very peripheral ones. Due to coherence, there are strong electromagnetic fields of short duration in such collisions. They give rise to photon-photon and photon-nucleus collisions with high flux up to an invariant mass region hitherto unexplored experimentally. After a general survey photon-photon luminosities in relativistic heavy ion collisions are discussed. Special care is taken to include the effects of strong interactions and nuclear size. Then photon-photon physics at various γγ-invariant mass scales is discussed. The region of several GeV, relevant for RHIC is dominated by QCD phenomena (meson and vector meson pair production). Invariant masses of up to about 100 GeV can be reached at LHC, and the potential for new physics is discussed. Photonuclear reactions and other important background effects, especially diffractive processes are also discussed. A special chapter is devoted to lepton-pair production, especially electron-positron pair production; due to the strong fields new phenomena, especially multiple e + e − pair production, will occur there.

In recent years, a large number of papers have appeared that dealt with e + e − pair production in heavy ion collisions at high energies. To a large extent these studies were motivated by the existence of relativistic heavy ion accelerators all over the world. There pair production can be studied in so called "ultra-peripheral collisions", where the ions do not come close enough to interact strongly with each other. Various different methods have been used and it is the purpose of this review to present a unified picture of the present status of the field. The lowest order Born result has been known for more than seven decades. The interest and focus is now on higher order effects for values of Zα < ∼ 1, where Z is the charge number of the ion. A similar problem appears for the Bethe-Heitler process, the production of e + e − pairs in photon-nucleus collisions. It was solved essentially some five decades ago by Bethe and Maximon. The result of Bethe and Maximon can also be recovered by summing over a class of Feynman diagrams to infinite order. These results can be used for a study of Coulomb corrections in nucleus-nucleus collisions. Indeed, the major part of these corrections have a structure closely related to the Bethe-Maximon solution. There are additional terms which give a small contribution to the total cross section at high energies. Their importance can be enhanced by concentrating on small impact parameters. An interesting exact solution of the one-particle Dirac equation in the high-energy limit was found independently by several authors. This led to some discussion about the interpretation of these results within QED and the correct regularization necessary to get the correct result. The dust of previous debates has settled and, indeed, a consistent picture has emerged. Another interesting higher order effect is multiple pair production, which we also discuss. We compare experimental results obtained recently at RHIC for free and bound-free pair production with theoretical results. We also make some more remarks on the physics of strong electric fields of longer duration. A new field is opened up by ultra-intense laser pulses. We argue that due to the short interaction time in ultraperipheral heavy ion pair production can be well understood in the frame of QED perturbation theory.

Effective γ-γ luminosities are calculated for various realistic hadron collider scenarios. The main characteristics of photon-photon processes at relativistic heavy-ion colliders are established and compared to the corresponding γ-γ-luminosities at e + -e − -and future Photon Linear Colliders (PLC). Higher order corrections as well as inelastic processes are discussed. It is concluded that feasible high luminosity Ca-Ca collisions at the Large Hadron Collider (LHC) are an interesting option for γ-γ physics up to about 100 GeV γ-γ CM energy. 25.75.+r,13.40.-f Typeset using REVT E X 1

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