New Schwinger-Dyson equations for non-Abelian gauge theories

Abstract

We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the standard case, the new series can be truncated gauge invariantly at any order in the dressed loop expansion. The construction is streamlined by resorting to the Batalin-Vilkovisky formalism which allows for a concise treatment of all the quantities appearing in the intermediate steps. The theoretical and phenomenological implications of this novel non-perturbative framework are discussed in detail.

84 pages, 29 figures; v.4 more typos corrected

Cited by in corpus (58)

• QCD and strongly coupled gauge theories: challenges and perspectives
• Pinch Technique: Theory and Applications
• Non-perturbative comparison of QCD effective charges
• Quark flavour effects on gluon and ghost propagators
• Running Gluon Mass from Landau Gauge Lattice QCD Propagator
• Chiral symmetry breaking with lattice propagators
• Effects of divergent ghost loops on the Green's functions of QCD
• QCD effective charges from lattice data
• Unquenching the gluon propagator with Schwinger-Dyson equations
• Gauge Sector Dynamics in QCD
• A new method for determining the quark-gluon vertex
• Refining the detection of the zero crossing for the symmetric and asymmetric three-gluon vertices
• The lattice gluon propagator in renormalizable $\xi$ gauges
• The all-order equation of the effective gluon mass
• Yang-Mills two-point functions in linear covariant gauges
• Discretization effects on renormalized gauge-field Green's functions, scale setting and gluon mass
• Gluon mass generation without seagull divergences
• Massless bound-state excitations and the Schwinger mechanism in QCD
• The dynamical equation of the effective gluon mass
• Emergent Hadron Mass in Strong Dynamics
• Indirect determination of the Kugo-Ojima function from lattice data
• Renormalization group analysis of the gluon mass equation
• Nonperturbative study of the four gluon vertex
• Schwinger mechanism in linear covariant gauges
• Nonperturbative structure of the ghost-gluon kernel
• Gluon mass generation in the massless bound-state formalism
• Evidence of ghost suppression in gluon mass dynamics
• Emergence of mass in the gauge sector of QCD
• Unified description of seagull cancellations and infrared finiteness of gluon propagators
• Coupled dynamics in gluon mass generation and the impact of the three-gluon vertex
• Gluon mass scale through nonlinearities and vertex interplay
• Gluon mass generation in the presence of dynamical quarks
• The Background Field Method as a Canonical Transformation
• QCD effective charge and the structure function $F_2$ at small-$x$
• AntiBRST symmetry and Background Field Method
• Gauge invariant Ansatz for a special three-gluon vertex
• Chiral symmetry breaking in QCD-like gauge theories with a confining propagator and dynamical gauge boson mass generation
• Comment on "Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure $SU(3)$ Yang-Mills Theory: Finite Lattice Spacing and Volume Effects"
• Practical scheme from QCD to phenomena via Dyson-Schwinger equations
• Positivity issues for the pinch-technique gluon propagator and their resolution
• Spontaneous chiral symmetry breaking in the massive Landau gauge: realistic running coupling
• Nonperturbative gluon and ghost propagators for d=3 Yang-Mills
• Gluon mass through ghost synergy
• QCD effective charge from the three-gluon vertex of the background-field method
• What Does Low Energy Physics Tell Us About The Zero Momentum Gluon Propagator
• Slavnov-Taylor constraints for non-trivial backgrounds
• Canonical Transformations and Renormalization Group Invariance in the presence of Non-trivial Backgrounds
• Gluon mass scale through the Schwinger mechanism
• Unraveling the organization of the QCD tapestry
• Schwinger-Dyson truncations in the all-soft limit: a case study
• From continuum QCD to hadron observables
• Vacuum energy as a c-function for theories with dynamically generated masses
• On aspects of self-consistency in the Dyson-Schwinger approach to QED and λ(ϕ^\star ϕ)^2 theories
• Patterns of gauge symmetry in the background field method
• Non-trivial Backgrounds in (non-perturbative) Yang-Mills Theory by the Slavnov-Taylor Identity
• Scrutinizing the Green's functions of QCD: Lattice meets Schwinger-Dyson
• The two-, three- and four-gluon sector of QCD in the Landau gauge
• A new method for computing the quark-gluon vertex