Obtaining fully polarised amplitudes in gauge invariant form

Abstract

We describe progress applying the Worldline Formalism of quantum field theory to the fermion propagator dressed by N -photons to study multi-linear Compton scattering processes, explaining how this approach -whose calculational advantages are well-known at multi-loop order -yields compact and manifestly gauge invariant scattering amplitudes.

Generalized LKF transformations for $N$-point fermion correlators in QED

“…In section II of [14], also in these proceedings, the worldline representation of the fermion propagator,…”

“…Noting that the worldline action S[x, ψ, A γ ] described in (3) of [14] is invariant under the supersymmetric transformations on the worldline (for Grassmann variable ζ)…”

“…where the insertion of Ā in the pre-factor of the kernel, in (1) of [14], is now generated by the functional derivative of the source,…”

“…x ′ π(i) xi i , as in (1) of [14], but now with A γ µ + Āµ instead of just A γ µ . The worldline representation of the N -point partial amplitude is…”

“…Interactions with external photons can be expressed in terms of the vertex operator in (5) of [14]. Then, a gauge transformation can be done by making the replacement ε µ → ε µ + ξk µ in the vertex operator and the on-shell invariance of the amplitude is well understood by the Ward-Takahashi identity.…”