Abstract
In this paper, I discuss inverse Compton scattering in a strong magnetic field. Using the standard technique in quantum electrodynamics, the solution of Dirac's equation for an electron in a uniform magnetic field and the accurate propagator of electron in a magnetic field, I have calculated the scattering matrix elements in the coordinate representation, the transition probabilities, and found the general formulae for the energy distribution of the scattered photons, and the differential and total scattering cross-sections.
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