Evaluation of QED cross sections in strong magnetic fields

Quantum electrodynamics (QED) becomes nonlinear when the magnetic field strength surpasses the critical Schwinger limit $B_Q \approx 4.41\cdot 10^{13}$ G. This limit is surpassed, for example, in the magnetospheres of a specific class of neutron stars known as magnetars, which has important consequences for magnetospheric plasma dynamics due to modifications in scattering cross sections. Using a formalism previously applied to the study of magnetic catalysis, I calculate the cross sections of all tree-level 1-to-2, 2-to-1, and 2-to-2 particle QED scattering processes that do not include a photon propagator. The calculations are done in a strong background magnetic field and the results are implemented into an open-source Python package. This article focuses on presenting the formalism and computational techniques required for the calculations, while the impact of the results on, e.g., magnetospheric plasma dynamics is discussed in a companion letter (Kiuru et al. 2026).