The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators

TL;DR

This paper derives a comprehensive non-perturbative gauge transformation framework for arbitrary N-point fermion correlators in QED, extending the Landau-Khalatnikov-Fradkin transformations beyond previous limitations.

Contribution

It introduces a generalized, exact non-perturbative LKF transformation applicable to any N-point fermion correlator in QED, including the dressed electron propagator.

Findings

Derived an exact non-perturbative LKF transformation for N-point functions.

Analyzed gauge transformation properties of dressed electron propagator.

Explored the structure of the LKF factor near two dimensions.

Abstract

We examine the non-perturbative gauge dependence of arbitrary configuration space fermion correlators in quantum electrodynamics (QED). First, we study the dressed electron propagator (allowing for emission or absorption of any number of photons along a fermion line) using the first quantised approach to quantum field theory and analyse its gauge transformation properties induced by virtual photon exchange. This is then extended to the $N$-point functions where we derive an exact, generalised version of the fully non-perturbative Landau-Khalatnikov-Fradkin (LKF) transformation for these correlators. We discuss some general aspects of application in perturbation theory and investigate the structure of the LKF factor about $D = 2$ dimensions.