Multiphoton amplitudes and generalized LKF transformation in Scalar QED

Abstract

We apply the worldline formalism to amplitudes in scalar quantum electrodynamics (QED) involving open scalar lines, with an emphasis on their non-perturbative gauge dependence. At the tree-level, we study the scalar propagator interacting with any number of photons in configuration space as well as in momentum space. At one-loop we rederive, in an efficient way, the off-shell vertex in an arbitrary dimension and any covariant gauge. Generalizing the Landau-Khalatnikov-Fradkin transformation (LKFT) for the non-perturbative propagator, we find simple non-perturbative transformation rules for arbitrary x-space amplitudes under a change of the covariant gauge parameter in terms of conformal cross ratios.

21 pages, 8 figures

References in corpus (6)

• Sketching the Bethe-Salpeter kernel
• Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators
• Gauge invariance of a critical number of flavours in QED3
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• 3-point off-shell vertex in scalar QED in arbitrary gauge and dimension
• Integral representations combining ladders and crossed-ladders

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• Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
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• Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes
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• Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED
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