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Using Hopf-algebraic structures as well as diagrammatic techniques for determining the Slavnov-Taylor identities for QCD we construct the relations for the triple and quartic gluon vertices at one loop. By making the longitudinal projection on an external gluon of a Greens function we show that the gluon self-energy of that leg is consistently replaced by a ghost self-energy. The resulting identities are then studied by evaluating all the graphs for an off-shell non-exceptional momentum configuration. In the case of the 3-point function this is for the most general momentum case and for the 4-point function we consider the fully symmetric point.
We study the solution to the Slavnov-Taylor (ST) identities in spontaneously broken effective gauge theories for a non-Abelian gauge group. The procedure to extract the $beta$-functions of the theory in the presence of (generalized) non-polynomial field redefinitions is elucidated.
We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in
The soft gluon limit of the longitudinal part of the quark-gluon vertex is studied by resorting to non-perturbative approaches to Quantum Chromodynamics (QCD). Based on a Slavnov-Taylor identity (STI), the longitudinal form factors is expressed in te
We clarify the derivation of high-energy QCD evolution equations from the fundamental gauge symmetry of QCD. The gauge-fixed classical action of the Color Glass Condensate (CGC) is shown to be invariant under a suitable BRST symmetry, that holds afte
We exploit the Ward-Slavnov-Taylor identity relating the 3-gluons to the ghost-gluon vertices to conclude either that the ghost dressing function is finite and non vanishing at zero momentum while the gluon propagator diverges (although it may do so