The photon polarization tensor in a homogeneous magnetic or electric field

TL;DR

This paper provides a detailed analytical study of the photon polarization tensor in homogeneous magnetic and electric fields, examining various regimes and critically reviewing approximation methods to improve understanding of its behavior.

Contribution

It offers a systematic, rigorous analysis of the photon polarization tensor across different regimes, including nonperturbative strong fields, and critically assesses existing approximation techniques.

Findings

Explicit analytical expressions for the polarization tensor in various regimes

Identification of the limitations of common approximation methods

Extension beyond traditional approximations in certain parameter regimes

Abstract

We revisit the photon polarization tensor in a homogeneous external magnetic or electric field. The starting point of our considerations is the momentum space representation of the one-loop photon polarization tensor in the presence of a homogeneous electromagnetic field, known in terms of a double parameter integral. Our focus is on explicit analytical insights for both on- and off-the-light-cone dynamics in a wide range of well-specified physical parameter regimes, ranging from the perturbative to the manifestly nonperturbative strong field regime. The basic ideas underlying well-established approximations to the photon polarization tensor are carefully examined and critically reviewed. In particular, we systematically keep track of all contributions, both the ones to be neglected and those to be taken into account explicitly, to all orders. This allows us to study their ranges of applicability in a much more systematic and rigorous way. We point out the limitations of such approximations and manage to go beyond at several instances.