A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations

TL;DR

This paper presents a new derivation of Landau-Khalatnikov-Fradkin transformations (LKFTs) for gauge and fermion fields, extending from Abelian QED to non-Abelian QCD, ensuring renormalizability and consistency.

Contribution

It introduces a gauge-invariant approach to derive LKFTs in both Abelian and non-Abelian gauge theories, a first in the rigorous formalism for non-Abelian cases.

Findings

First rigorous construction of non-Abelian LKFTs

Demonstrates renormalizability to all orders

Provides a path integral derivation confirming consistency

Abstract

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.