Photon splitting in strong magnetic fields

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Abstract
Using the formalism of relativistic quantum field theory we derive the probability for the splitting of one photon into two photons in the presence of a uniform magnetic field. We express the electron propagator in a magnetic field in terms of Landau spinors in configuration space and obtain an analytical expression for the S-matrix element of the third-order process which is exact in the magnetic field strength as well as the photon energy, and lends itself to numerical evaluation. Numerical results are presented for the splitting probability as a function of photon energy below the pair creation threshold for different neutron star magnetic field strengths. Our results open the way to quantitative studies of the signature of photon splitting in the γ-ray spectra of compact cosmic objects.