  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.
