On analytic properties of the photon polarization function in a background magnetic field

We examine the analytic properties of the photon polarization function in a background magnetic field, using the technique of inverse Mellin transform. The photon polarization function is first expressed as a power series of the photon energy ω with ω<2me. Based upon this energy expansion and the branch cut of the photon polarization function in the complex ω plane, we compute the absorptive part of the polarization function with the inverse Mellin transform. Our results are valid for arbitrary photon energies and magnetic-field strengths. The applications of our approach are briefly discussed.