Abstract
The Landau-Khalatnikov-Fradkin transformations (LKFTs) represent an important tool for probing the gauge dependence of the correlation functions within the class of linear covariant gauges. Recently these transformations have been derived from first principles in the context of non-Abelian gauge theory (QCD) introducing a gauge invariant transverse gauge field expressible as an infinite power series in a Stueckelberg field. In this work we explicitly calculate the transformation for the gluon propagator, reproducing its dependence on the gauge parameter at the one loop level and elucidating the role of the extra fields involved in this theoretical framework. Later on, employing a unifying scheme based upon the BRST symmetry and a resulting generalized Slavnov-Taylor identity, we establish the equivalence between the LKFTs and the Nielsen identities which are also known to connect results in different gauges.
Highlights
Later on, employing a unifying scheme based upon the Becchi-Rouet-StoraTyutin symmetry and a resulting generalized Slavnov-Taylor identity, we establish the equivalence between the Landau-Khalatnikov-Fradkin transformations (LKFTs) and the Nielsen identities which are known to connect results in different gauges
Gauge symmetries are a ubiquitous feature in our theoretical understanding of physical interactions at their fundamental level
In the non-Abelian case (QCD) the constraints imposed by the gauge transformations on the correlation functions have been mainly studied in the form of the Slavnov-Taylor identities [22]
Summary
Gauge symmetries are a ubiquitous feature in our theoretical understanding of physical interactions at their fundamental level. In the non-Abelian case (QCD) the constraints imposed by the gauge transformations on the correlation functions have been mainly studied in the form of the Slavnov-Taylor identities [22] (their Abelian counterpart are the WardTakahashi identities [23]) These identities can be derived by exploiting the invariance of the effective action under the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformation [24] which guarantees the renormalizabilty of the theory. In [41], a derivation of the LKFTs for the n-point correlation functions has been detailed, employing gauge invariant composite operators Ahμ and ψh which involve a Stueckelberg type scalar field These composite fields, originally introduced in an attempt to construct gauge invariant colored states [42], have recently received a renewed spotlight in the context of gauge-fixing procedure at a nonperturbative level. Using the extended source formalism, we discuss and establish the equivalence between the LKFTs and the Nielsen identities
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