  The presence of strong electromagnetic fields adds huge complexity to QED
Feynman diagrams, such that new methods are required to calculate higher-loop
and higher-multiplicity scattering amplitudes. Here we use the worldline
formalism to present `Master Formulae' for all tree level amplitudes of two
massive particles and an arbitrary number of photons, in a plane wave
background, in both scalar and spinor QED. The plane wave is treated without
approximation throughout, meaning in particular that our formulae are valid in
the strong-field regime of current theoretical and experimental interest. We
check our results against literature expressions obtainable at low multiplicity
via direct Feynman diagram calculations.
