A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations

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.

arXiv comment16 pages

References in corpus (78)

• 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
• Aspects of the Functional Renormalisation Group
• Local BRST cohomology in gauge theories
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Baryons as relativistic three-quark bound states
• On the infrared behavior of Landau gauge Yang-Mills theory
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Pinch Technique: Theory and Applications
• Measurement of the gamma gamma* --> pi0 transition form factor
• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Charged pion form factor between Q^2=0.60 and 2.45 GeV^2. II. Determination of, and results for, the pion form factor
• Landau gauge Yang-Mills correlation functions
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• The Gribov problem and QCD dynamics
• On the Significance of the Quantity "A Squared"
• Short-distance tachyonic gluon mass and 1/Q^2 corrections
• Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
• Measurement of gamma gamma* --> pi0 transition form factor at Belle
• Gauge bosons at zero and finite temperature
• Constituent Quarks from QCD
• On the IR behaviour of the Landau-gauge ghost propagator
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Pion electromagnetic form factor at spacelike momenta
• The Infrared Behaviour of the Pure Yang-Mills Green Functions
• On the Emerging Phenomenology of <(A_μ)^2>
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Testing Landau gauge OPE on the Lattice with a $<A^2>$ Condensate
• Three-point vertices in Landau-gauge Yang-Mills theory
• 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
• Gluonic three-point correlations in pure Landau gauge QCD
• The strong coupling and its running to four loops in a minimal MOM scheme
• Structure of the neutral pion and its electromagnetic transition form factor
• Källén-Lehmann spectroscopy for (un)physical degrees of freedom
• An exact nilpotent non-perturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge
• Three-gluon vertex in arbitrary gauge and dimension
• Natural constraints on the gluon-quark vertex
• Gribov copies, Lattice QCD and the gluon propagator
• Dynamical chiral symmetry breaking and the fermion--gauge-boson vertex
• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
• Gauge independent Chiral Symmetry Breaking in Quenched QED
• On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations
• Gauge invariance of a critical number of flavours in QED3
• Covariant gauge on the lattice: a new implementation
• The lattice gluon propagator in renormalizable $\xi$ gauges
• Yang-Mills two-point functions in linear covariant gauges
• 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
• On gluon and ghost propagators in linear covariant gauges
• Infrared Features of the Landau Gauge QCD
• Quark-gluon Vertex: A Perturbation Theory Primer and Beyond
• Revealing dressed-quarks via the proton's charge distribution
• 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
• Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics
• Schwinger mechanism in linear covariant gauges
• The Nielsen Identities for the Two-Point Functions of QED and QCD
• The gluon propagator in Feynman gauge by the method of stationary variance
• Quark-gluon vertex from the Landau gauge Curci-Ferrari model
• Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3
• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• Charges in Gauge Theories
• Multiphoton amplitudes and generalized LKF transformation in Scalar QED
• A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges
• Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation
• Second order gluon polarization for SU(N) theory in linear covariant gauge
• Local Gauge Transformation for the Quark Propagator in an SU(N) Gauge Theory
• The nonperturbative propagator and vertex in massless quenched QED_d
• Feynman gauge on the lattice: new results and perspectives
• On the gauge parameter dependence of QED
• 3-point off-shell vertex in scalar QED in arbitrary gauge and dimension
• Landau-Khalatnikov-Fradkin transformation for the fermion propagator in QED in arbitrary dimensions
• Gauge copies in the Landau-DeWitt gauge: a background invariant restriction
• Constructing Scalar-Photon Three Point Vertex in Massless Quenched Scalar QED
• On a renormalizable class of gauge fixings for the gauge invariant operator $A_{\min }^2$
• Gauge covariance of the fermion Schwinger-Dyson equation in QED

Cited by in corpus (14)

• Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking
• Landau-Khalatnikov-Fradkin transformation and the mystery of even $\zeta$-values in Euclidean massless correlators
• 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
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator
• Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
• Landau-Khalatnikov-Fradkin Transformation and Even zeta Functions
• An all order renormalizable Refined-Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges
• Landau-Khalatnikov-Fradkin transformation and hatted zeta-values
• Gauge covariance of the gap equation: from the rainbow truncation to gauge symmetry constraints