We apply the worldline formalism to scalar quantum electrodynamics (QED) to find a Bern–Kosower type master formula for generalized Compton scattering, on-shell and off-shell. Moreover, we use it to study the non-perturbative gauge parameter dependence of amplitudes in scalar QED and, as our main result, find a simple non-perturbative transformation rule under changes of this parameter in x-space in terms of conformal cross ratios. This generalizes the well-known Landau–Khalatnikov–Fradkin transformation (LKFT). We also exemplify how this generilized LKFT works in perturbation theory.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 28–34, November, 2016.
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Ahmadiniaz, N., Bashir, A. & Schubert, C. Multiphoton Amplitudes and Generalized LKF Transformation in Scalar QED Using the Worldline Formalism. Russ Phys J 59, 1752–1760 (2017). https://doi.org/10.1007/s11182-017-0973-2
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DOI: https://doi.org/10.1007/s11182-017-0973-2