Fresh look at the Abelian and non-Abelian Landau-Khalatnikov-Fradkin transformations

Meerleer, T. De; Dudal, David; Sorella, S. P.; Dall’Olio, Pietro; Bashir, Adnan

doi:10.1103/physrevd.97.074017

Cited by 22 publications

(38 citation statements)

References 89 publications

(168 reference statements)

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“…As a final step, we took the Fourier transform back to momentum space and obtained S F (p, ξ) with P (p, ξ) in (15). Let us also note that expansions similar to (13) and (16) can also be expressed in Minkowski space with the help of the replacement p 2 → −p 2 .…”

Section: B Lkf Transformation In Momentum Spacementioning

confidence: 99%

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

2020

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We study the gauge-covariance of the massless fermion propagator in reduced Quantum Electrodynamics (QED). Starting from its value in some gauge, we evaluate an all order expression for it in another gauge by means of the Landau-Khalatnikov-Fradkin (LKF) transformation. We find that the weak coupling expansions thus derived are in perfect agreement with the exact calculations. We also prove that the fermion anomalous dimension of reduced QED is gauge invariant to all orders of perturbation theory except for the first one.

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Section: B Lkf Transformation In Momentum Spacementioning

confidence: 99%

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

2020

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“…Although the addition of S h to the classical action does not change the physical content of the theory and appears to present a pointless complication, the introduction of the gauge invariant field A h μ makes it straightforward to derive the gauge covariance of the correlation functions (see [41] for an alternative derivation based on functional integration). In fact, we can define the corresponding gauge invariant operators for the fermion fields…”

Section: Landau-khalatnikov-fradkin Transformationsmentioning

confidence: 99%

“…In [41], a derivation of the LKFTs for the n-point correlation functions has been detailed, employing gauge invariant composite operators A h μ and ψ h 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.…”

Section: Introductionmentioning

confidence: 99%

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Landau-Khalatnikov-Fradkin transformations, Nielsen identities, their equivalence, and implications for QCD

Meerleer

Dudal

Sorella³

et al. 2020

Phys. Rev. D

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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 Becchi-Rouet-Stora-Tyutin 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.

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“…therein. Another potential fruitful application can be figure out in relationship to the non-Abelian Landau-Khalatnikov-Fradkin transformations (LKF) along the path outlined in [40], where the localized BRST invariant composite field A h µ was employed to interpolate the n-point correlation functions of the gauge field A µ between different gauges. In this case, the composite invariant field ψ h could allow to generalize the construction of [40] to the LKF transformations for correlation functions including spinor fields within a BRST invariant renormalizable framework.…”

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confidence: 99%

Study of a gauge invariant local composite fermionic field

2020

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In this work, we study a gauge invariant local non-polynomial composite spinor field in the fundamental representation in order to establish its renormalizability. Similar studies were already done in the case of pure Yang-Mills theories where a local composite gauge invariant vector field was obtained and an invariant renormalizable mass term could be introduced. Our model consists of a massive Euclidean Yang-Mills action with gauge group SU (N ) coupled to fermionic matter in the presence of an invariant spinor composite field and quantized in the linear covariant gauges. The whole set of Ward identities is analysed and the algebraic proof of the renormalizability of the model is obtained to all orders in a loop expansion. I. INTRODUCTIONThe theoretical studies of quantum chromodynamics (QCD) in the low energy regime, where nonperturbative phenomena like confinement take place, still lack a satisfactory understanding.Besides quark confinement, let us underline that the gluon confinement is still a challenging, yet unsolved, issue. Several nonperturbative techniques based on the studies of the Dyson-Schwinger equations, functional renormalization group, Kugo-Ojima criterion, Gribov-Zwanziger approach and its refined version, have provided a fruitful ground for a better understanding of the behaviour of the two-point Landau gauge gluon correlation function in the infrared region, see . The output of these investigations is in quite good agreement with the lattice data on the gluon propagator, which exhibit a violation of the reflection positivity [26][27][28][29][30]. This peculiar behaviour of the gluon propagator is commonly interpreted as a signal of gluon confinement, due to the impossibility of attaching a physical meaning to the gluon as an excitation of the spectrum of the theory.

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Fresh look at the Abelian and non-Abelian Landau-Khalatnikov-Fradkin transformations

Cited by 22 publications

References 89 publications

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED

Landau-Khalatnikov-Fradkin transformations, Nielsen identities, their equivalence, and implications for QCD

Study of a gauge invariant local composite fermionic field

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