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The presence of strong electromagnetic fields adds huge complexity to QEDFeynman diagrams, such that new methods are required to calculate higher-loopand higher-multiplicity scattering amplitudes. Here we use the worldlineformalism to present `Master Formulae' for all tree level amplitudes of twomassive particles and an arbitrary number of photons, in a plane wavebackground, in both scalar and spinor QED. The plane wave is treated withoutapproximation throughout, meaning in particular that our formulae are valid inthe strong-field regime of current theoretical and experimental interest. Wecheck our results against literature expressions obtainable at low multiplicityvia direct Feynman diagram calculations.

Master Formulae for $N$-photon tree level amplitudes in plane wave backgrounds