  We evaluate several basic electrodynamic processes as modified by the
presence 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 dissipative
phenomena outside magnetars and some other neutron stars. Differential and
total cross sections and rates are presented for electron-photon scattering,
the annihilation of an electron-positron pair into two photons, the inverse
process of two-photon pair creation, and single-photon pair creation into the
lowest Landau state. The relative importance of these interactions changes as
the background magnetic field grows in strength. The particle phase space
relevant for a given process may be restricted by single-photon pair creation,
which also opens up efficient channels for pair multiplication, e.g. in
combination with scattering. Our results are presented in the form of compact
formulae that allow for relativistic electron (positron) motion, in the regime
where Landau excitations can be neglected (corresponding to $10^3B_{\rm Q} \gg
B \gg B_{\rm Q}$ for moderately relativistic motion along the magnetic field).
Where a direct comparison is possible, our results are tested against earlier
calculations, and a brief astrophysical context is provided. A companion paper
considers electron-positron scattering, scattering of electrons and positrons
by ions, and relativistic electron-ion bremsstrahlung.

High Energy Astrophysical Phenomena