The effect of radiation corrections to the mass of an electron and positron on the polarization operator of a photon in a magnetic field

TL;DR

This paper investigates how radiation corrections influence the polarization operator of a photon in a magnetic field, providing a comprehensive formula that accounts for radiation effects and level overlaps in both weak and strong fields.

Contribution

It introduces a general formula for the photon polarization operator that includes radiation effects and addresses divergence issues at thresholds in magnetic fields.

Findings

Radiation effects regularize diverging threshold terms.

Conditions for complete Landau level overlap are formulated.

The semiclassical operator method's applicability is clarified.

Abstract

The polarization operator of a photon in a constant and uniform magnetic field is studied taking into account the radiation width and shift of the Landau levels in both weak and strong fields compared with the critical field $H_0=4,41\cdot10^{13}$ G . A general formula is obtained for the polarization operator of a photon in which radiation effects are taken into account. Now diverging previously threshold terms have a finite value. The conditions are formulated under which the energy levels completely overlap, and thereby the most appropriate application of the semiclassical operator method to the problem under study becomes.