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We apply the worldline formalism to scalar quantum electrodynamics (QED) tofind a Bern-Kosower type master formula for generalized Compton scattering,on-shell and off-shell. Moreover, we use it to study the non-perturbative gaugeparameter dependence of amplitudes in scalar QED and, as our main result, finda simple non-perturbative transformation rule under changes of this parameterin x-space in terms of conformal cross ratios. This generalizes the well-knownLandau-Khalatnikov-Fradkin transformation (LKFT). We also exemplify how theLKFT works in perturbation theory.

Multiphoton amplitudes and generalized LKF transformation in scalar QED using the worldline formalism