| Summary: | The Bern-Kosower formalism, originally developed around 1990 as a novel way of obtaining on-shell amplitudes in field theory as limits of string amplitudes, has recently been shown to be extremely effcient as a tool for obtaining form factor decompositions of the N - gluon vertices. Its main advantages are that gauge invariant structures can be generated by certain systematic integration-by-parts procedures, making unnecessary the usual tedious analysis of the non-abelian off-shell Ward identities, and that the scalar, spinor and gluon loop cases can be treated in a unified way. After discussing the method in general for the N - gluon case, I will show in detail how to rederive the Ball- Chiu decomposition of the three - gluon vertex, and finally present two slightly different decompositions of the four - gluon vertex, one generalizing the Ball Chiu one, the other one closely linked to the QCD effective action.
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