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.
Highlights
When we study strong color interaction, quantum chromodynamics (QCD), we start from the most basic fields, namely the quarks, gluons and the FaddeevPopov ghosts in 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 Landau-Khalatnikov-Fradkin transformations (LKFTs)
This non-Abelian LKFT law is in perfect agreement with the alternative derivation with the gauge invariant fermion field ψh that resulted in Eq (28)
Summary
When we study strong color interaction, quantum chromodynamics (QCD), we start from the most basic fields, namely the quarks, gluons and the FaddeevPopov ghosts in covariant gauges. There is a large body of work which has used these transformations as a guiding principle toward an improved Ansatz for the three-point vertex and imposing gauge invariant chiral symmetry breaking; see for example [19,58,59,60]. These transformations have been studied in the world line formalism, where LKFTs are generalized to arbitrary amplitudes in scalar QED [61].
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