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Gauge invariance and soft limits can be enough to determine the analyticstructure of scattering amplitudes in certain theories. This prompts thequestion of how gauge invariance is connected to analytic structure in moregeneral theories. Here we focus on QED in background plane waves. We show thatimposing gauge invariance introduces new virtuality poles into internal momentaon which amplitudes factorise into a series of terms. Each term is gaugeinvariant, has a different analytic structure in external momenta, and exhibitsa hard/soft factorisation. The introduced poles are dictated by infra-redbehaviour, which allows us to extend our results to scalar Yukawa theory. Thebackground is treated non-perturbatively throughout.

The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red