On the self-consistency of off-shell Slavnov-Taylor identities in QCD

Abstract

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 Green's 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.

arXiv comment48 latex pages, 8 figures, 6 tables, anc directory contains txt file with electronic version of amplitudes and projection matrices, minor text changes and extra references added

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• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Off-shell Ward identities for N-gluon amplitudes
• Off-shell Diagrammatics for Quantum Gravity
• Propagator-cancelling scalar fields