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Master formulas for the dressed scalar propagator in a constant field. (English) Zbl 1361.81163
Summary: The worldline formalism has previously been used for deriving compact master formulas for the one-loop N-photon amplitudes in both scalar and spinor QED, and in the vacuum as well as in a constant external field. For scalar QED, there is also an analogous master formula for the propagator dressed with \(N\) photons in the vacuum. Here, we extend this master formula to include a constant field. The two-photon case is worked out explicitly, yielding an integral representation for the Compton scattering cross section in the field suitable for numerical integration in the full range of electric and magnetic field strengths.

MSC:
81V10 Electromagnetic interaction; quantum electrodynamics
81U05 \(2\)-body potential quantum scattering theory
81T18 Feynman diagrams
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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