Polarization operator for plane-wave background fields

TL;DR

This paper presents a new symmetric representation of the leading-order polarization operator in strong-field QED with plane-wave backgrounds, derived via direct Feynman diagram evaluation using Volkov states.

Contribution

It introduces an alternative, symmetric formulation of the polarization operator and confirms the Ward-Takahashi identity in this context, advancing theoretical understanding.

Findings

Derived a symmetric representation of the polarization operator

Validated the Ward-Takahashi identity for loop diagrams in plane-wave backgrounds

Provided a direct Feynman diagram evaluation method

Abstract

We derive an alternative representation of the leading-order contribution to the polarization operator in strong-field quantum electrodynamics with a plane-wave electromagnetic background field, which is manifestly symmetric with respect to the external photon momenta. Our derivation is based on a direct evaluation of the corresponding Feynman diagram, using the Volkov representation of the dressed fermion propagator. Furthermore, the validity of the Ward-Takahashi identity is shown for general loop diagrams in an external plane-wave background field.