Polarization operator of a photon in a magnetic field

Abstract

The polarization operator of a photon in a static uniform magnetic field has been studied at photon energies both above and below the threshold of electron–positron pair production by a photon. In the first order of the fine-structure constant α, expressions for the refractive index of a photon with a certain polarization in both low and high fields as compared to the critical field H₀ = 4.41 × 10¹³ G have been obtained. Both the purely quantum range of photon energies, where the particles of a pair are produced at the lowest Landau levels, and the region of applicability of the semiclassical approximation in the case of the population of high energy levels have been considered. A general spectral integral formula has been obtained with divergent threshold terms separated in an explicit form.