  The worldline formalism has previously been used for deriving compact master
formulas for the one-loop N-photon amplitudes in both scalar and spinor QED,
and in the vacuum as well as in a constant external field. For scalar QED,
there is also an analogous master formula for the propagator dressed with N
photons in the vacuum. Here, we extend this master formula to include a
constant field. The two-photon case is worked out explicitly, yielding an
integral representation for the Compton scattering cross section in the field
suitable for numerical integration in the full range of electric and magnetic
field strengths.
