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Register a new userOn Analytic Properties of the Photon Polarization Function in a Background Magnetic Field
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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 $omega$ with $omega< 2m_e$. Based upon this energy expansion and the branch cut of the photon polarization function in the complex $omega$ 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.
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We develop the technique of inverse Mellin transform for processes occurring in a background magnetic field. We show by analyticity that the energy (momentum) derivatives of a field theory amplitude at the zero energy (momentum) is equal to the Mellin transform of the absorptive part of the amplitude. By inverting the transform, the absorptive part of the amplitude can be easily calculated. We apply this technique to calculate the photon polarization function in a background magnetic field.
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