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The Landau-Khalatnikov-Fradkin transformations (LKFTs) represent an importanttool for probing the gauge dependence of the correlation functions within theclass of linear covariant gauges. Recently these transformations have beenderived from first principles in the context of non-Abelian gauge theory (QCD)introducing a gauge invariant transverse gauge field expressible as an infinitepower series in a Stueckelberg field. In this work we explicitly calculate thetransformation for the gluon propagator, reproducing its dependence on thegauge parameter at the one loop level and elucidating the role of the extrafields involved in this theoretical framework. Later on, employing a unifyingscheme based upon the BRST symmetry and a resulting generalized Slavnov-Tayloridentity, we establish the equivalence between the LKFTs and the Nielsenidentities which are also known to connect results in different gauges.

Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD