Gauge-invariant four-gluon vertex and its Ward identity

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Abstract
We use the S-matrix pinch technique to construct at one-loop order a four-gluon vertex for QCD, which is independent of the choice of the gauge parameter, when one or more of the incoming momenta are off shell. We discuss some of the technical subtleties in the application of the pinch technique and show that this vertex satisfies a very simple Ward identity, relating it to a previously constructed gauge-independent three-gluon vertex, also found with the same technique. This analysis serves as a prelude to the construction of an effective potential for QCD, which is gauge-independent order by order in the dressed-loop expansion.