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We evaluate several basic electrodynamic processes as modified by thepresence of a very strong magnetic field, exceeding $B_{\rm Q} \equiv m^2/e =4.4\times 10^{13}$ G. These results are needed to build models of dissipativephenomena outside magnetars and some other neutron stars. Differential andtotal cross sections and rates are presented for electron-photon scattering,the annihilation of an electron-positron pair into two photons, the inverseprocess of two-photon pair creation, and single-photon pair creation into thelowest Landau state. The relative importance of these interactions changes asthe background magnetic field grows in strength. The particle phase spacerelevant for a given process may be restricted by single-photon pair creation,which also opens up efficient channels for pair multiplication, e.g. incombination with scattering. Our results are presented in the form of compactformulae that allow for relativistic electron (positron) motion, in the regimewhere Landau excitations can be neglected (corresponding to $10^3B_{\rm Q} \ggB \gg B_{\rm Q}$ for moderately relativistic motion along the magnetic field).Where a direct comparison is possible, our results are tested against earliercalculations, and a brief astrophysical context is provided. A companion paperconsiders electron-positron scattering, scattering of electrons and positronsby ions, and relativistic electron-ion bremsstrahlung.

QED Phenomena in an Ultrastrong Magnetic Field. I. Electron-Photon Scattering, Pair Creation, and Annihilation