Multiphoton amplitudes and generalized LKF transformation in Scalar QED

TL;DR

This paper uses the worldline formalism to analyze gauge dependence in scalar QED amplitudes, deriving non-perturbative transformation rules for propagators and vertices under gauge changes.

Contribution

It introduces a novel application of the worldline formalism to scalar QED, deriving non-perturbative gauge transformation rules for amplitudes.

Findings

Derived non-perturbative gauge transformation rules for scalar QED propagators.

Rederived the off-shell vertex in arbitrary dimensions and gauges.

Established simple transformation rules using conformal cross ratios.

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.