One loop photon-graviton mixing in an electromagnetic field: Part 1

TL;DR

This paper addresses the one-loop photon-graviton mixing amplitude in an external constant electromagnetic field, focusing on virtual charged scalar or spinor loops. It employs the worldline (string-inspired) formalism to derive covariant, compact $2$-parameter integral representations valid for arbitrary photon energies and field strengths. The authors verify gauge and gravitational Ward identities and show consistency with the low-energy effective action, providing a solid theoretical foundation for the results. The work sets the stage for Part II, which will perform numerical analyses of photon-graviton conversion in magnetic fields and discuss potential astrophysical implications.

Abstract

Photon-graviton mixing in an electromagnetic field is a process of potential interest for cosmology and astrophysics. At the tree level it has been studied by many authors. We consider the one-loop contribution to this amplitude involving a charged spin 0 or spin 1/2 particle in the loop and an arbitrary constant field. In the first part of this article, the worldline formalism is used to obtain a compact two-parameter integral representation for this amplitude, valid for arbitrary photon energies and background field strengths. The calculation is manifestly covariant througout.