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

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.

arXiv comment18 pages

References in corpus (59)

• FeynRules 2.0 - A complete toolbox for tree-level phenomenology
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• New Developments in FeynCalc 9.0
• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• The Stueckelberg Field
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• On the Significance of the Quantity "A Squared"
• Short-distance tachyonic gluon mass and 1/Q^2 corrections
• Constituent Quarks from QCD
• Quark flavour effects on gluon and ghost propagators
• On the Emerging Phenomenology of <(A_μ)^2>
• Testing Landau gauge OPE on the Lattice with a $<A^2>$ Condensate
• An Infrared Safe perturbative approach to Yang-Mills correlators
• The lattice Landau gauge gluon propagator: lattice spacing and volume dependence
• The non-perturbative groundstate of Q.C.D and the local composite operator A_mu^2
• A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations
• The Nielsen Identities of the SM and the definition of mass
• Chiral symmetry breaking with lattice propagators
• An exact nilpotent non-perturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge
• Dynamical chiral symmetry breaking and the fermion--gauge-boson vertex
• Practical corollaries of transverse Ward-Green-Takahashi identities
• Gauge independent Chiral Symmetry Breaking in Quenched QED
• Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators
• Gauge invariance of a critical number of flavours in QED3
• Analytical study of Yang-Mills theory in the infrared from first principles
• A local and BRST-invariant Yang-Mills theory within the Gribov horizon
• Gauge covariance and the fermion-photon vertex in three- and four- dimensional, massless quantum electrodynamics
• Quark-gluon Vertex: A Perturbation Theory Primer and Beyond
• Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model
• More on the non-perturbative Gribov-Zwanziger quantization of linear covariant gauges
• Non-perturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST invariant two-point correlation function
• Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta
• Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics
• Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3
• Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking
• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• Non-perturbative Fermion Propagator for the Massless Quenched QED3
• Multiphoton amplitudes and generalized LKF transformation in Scalar QED
• Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation
• A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges
• Dynamical Fermion Masses and Constraints of Gauge Invariance in Quenched QED3
• Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
• Local Gauge Transformation for the Quark Propagator in an SU(N) Gauge Theory
• The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories
• Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators
• The nonperturbative propagator and vertex in massless quenched QED_d
• 3-point off-shell vertex in scalar QED in arbitrary gauge and dimension
• On the gauge parameter dependence of QED
• A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations
• Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions
• Gauge Covariance Relations and the Fermion Propagator in Maxwell-Chern-Simons QED3
• On a renormalizable class of gauge fixings for the gauge invariant operator $A_{\min }^2$
• Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED
• Gauge covariance of the fermion Schwinger-Dyson equation in QED
• Canonical Flow in the Space of Gauge Parameters

Cited by in corpus (10)

• Gauge Sector Dynamics in QCD
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
• Effect of the Quark-Gluon Vertex on Dynamical Chiral Symmetry Breaking
• The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
• Gauge dependence of the quark gap equation: an exploratory study
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
• Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator
• An all order renormalizable Refined-Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges
• Gauge covariance of the gap equation: from the rainbow truncation to gauge symmetry constraints