Polarization operator of a photon in a magnetic field

TL;DR

This paper investigates the polarization operator of a photon in a magnetic field across different energy regimes, providing approximate formulas for weak and strong fields and a general expression for the photon’s effective mass.

Contribution

It derives a comprehensive formula for the photon polarization operator in a magnetic field at arbitrary energies, including approximations for different field strengths and energy regions.

Findings

Derived approximate expressions for weak and strong magnetic fields.

Obtained a general formula for the photon’s effective mass with polarization dependence.

Analyzed photon behavior near pair creation threshold and at high energies.

Abstract

In the first order of the fine structer constant, the polarization operator of a photon is investigated in a constant and homogeneous magnetic field at arbitrary photon energies. For weak and strong fields H, compared with the Schwinger critical field, approximate expressions have been found. We consider the pure quantum region of photon energy near the threshold of pair creation, as well as the region of high energy levels where the quasiclassical approximation is valid. The general formula has been obtained for the effective mass of photon with given polarization. It is useful for an analysis of the problem under consideration on the whole and at a numerical work