On structure of the polarization operator in a magnetic field

TL;DR

This paper analyzes the polarization operator of photons in a magnetic field, deriving expressions for the effective photon mass across quantum and quasiclassical energies, including threshold singularities.

Contribution

It provides a comprehensive investigation of the polarization operator at arbitrary photon energies in a magnetic field below the Schwinger limit, with new formulas accounting for threshold effects.

Findings

Derived expressions for the polarization operator in different energy regimes.

Identified singular terms at electron-positron creation thresholds.

Extended understanding of photon behavior in magnetic fields.

Abstract

The polarization operator is investigated at arbitrary photon energy in a constant and homogeneous magnetic field for the strength H less than the Schwinger critical value. The effective mass of a real photon with a preset polarization is considered in the quantum energy region as well as in the quasiclassical one. Obtained in the quantum region expressions include the singular terms at the creation threshold of electron and positron on Landau levels.