Spectral-integral representation of the photon polarization operator in a constant uniform magnetic field

TL;DR

This paper derives a comprehensive spectral-integral representation of the photon polarization operator in a uniform magnetic field, applicable across all photon energies and field strengths, facilitating analysis of photon behavior in quantum and classical regimes.

Contribution

It introduces a general formula for the photon effective mass in a magnetic field, valid at arbitrary energies and field strengths, including approximate expressions for strong and weak fields.

Findings

Derived a spectral-integral representation valid for all energies and field strengths.

Provided approximate formulas for strong and weak magnetic fields.

Analyzed photon behavior in quantum and quasiclassical regimes.

Abstract

The polarization operator in a constant and homogeneous magnetic field of arbitrary strength is investigated on mass shell. The calculations are carried out at all photon energies higher the pair creation threshold as well as lower this threshold. The general formula for the effective mass of the photon with given polarization has been obtained being useful for an analysis of the problem under consideration as well as at a numerical work. Approximate expressions for strong or weak fields, compared with the critical field, have been found. Depending on the ratio of these fields we consider the pure quantum region of photon energy, where particles are created on lower Landau levels or created not at all. Also the energy region of large level numbers is considered where the quasiclassical approximation is valid.