Transverse Symmetry Transformations and the Quark-Gluon Vertex Function in QCD

Abstract

The transverse symmetry transformations associated with the normal symmetry transformations in gauge theories are introduced, which at first are used to reproduce the transverse Ward-Takahashi identities in the Abelian theory QED. Then the transverse symmetry transformations associated with the BRST symmetry and chiral transformations in the non-Abelian theory QCD are used to derive the transverse Slavnov-Taylor identities for the vector and axial-vector quark-gluon vertices, respectively. Based on the set of normal and transverse Slavnov-Taylor identities, an expression of the quark-gluon vertex function is derived, which describes the constraints on the structure of the quark-gluon vertex imposed from the underlying gauge symmetry of QCD alone. Its role in the study of the Dyson-Schwinger equation for the quark propagator in QCD is discussed.

13 pages, no figure

References in corpus (15)

• 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
• Dyson-Schwinger equations: a tool for hadron physics
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
• Nonperturbative structure of the quark-gluon vertex
• Quark-gluon vertex in arbitrary gauge and dimension
• Quark-gluon vertex model and lattice-QCD data
• Aspects of the confinement mechanism in Coulomb-gauge QCD
• Infrared Behaviour of Propagators and Vertices
• Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions
• Identical Relations among Transverse Parts of Variant Green Functions and the Full Vertices in Gauge Theories
• A Note on Transverse Axial Vector and Vector Anomalies in U(1) Gauge Theories
• Transverse Ward-Takahashi Relation for the Fermion-Boson Vertex Function in 4-dimensional QED
• Quantum anomaly of the transverse Ward-Takahashi relation for the axial-vector vertex

Cited by in corpus (20)

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• Dynamical chiral symmetry breaking and the fermion--gauge-boson vertex
• Practical corollaries of transverse Ward-Green-Takahashi identities
• QCD phase transitions via a refined truncation of Dyson-Schwinger equations
• Pseudoscalar glueball mass: a window on three-gluon interactions
• Quark-gluon vertex from Nf=2 lattice QCD
• Excited hadrons and the analytical structure of bound-state interaction kernels
• Interplay of dynamical and explicit chiral symmetry breaking effects on a quark
• The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
• Gauge dependence of the quark gap equation: an exploratory study
• The Quark Propagator in a Truncation Scheme beyond the Rainbow Approximation
• Temperature Dependence of the Effective Bag Constant and the Radius of a Nucleon in the Global Color Symmetry Model of QCD
• Calculation of tensor susceptibility beyond rainbow-ladder approximation of Dyson-Schwinger equations approach
• A Universal Constraint on the Infrared Behavior of the Ghost Propagator in QCD
• Thermodynamics of the most generalized form of Holographic Dark Energy and some particular cases with Corrected Entropies
• Transverse Ward-Takahashi Identities and Full Vertices Functions in Different Representation in QED${}_3$
• Derivation of the gap and Bethe-Salpeter equations at large $N_c$ limit and symmetry preserving truncations
• Beyond Symmetries : Anomalies in Transverse Ward--Takahashi Identities
• Gauge covariance of the gap equation: from the rainbow truncation to gauge symmetry constraints