A multiple commutator formula for the sum of Feynman diagrams

In the presence of a large parameter, such as mass or energy, leading behavior of individual Feynman diagrams often get canceled in the sum. This is known to happen in large-Nc QCD in the presence of a baryon, and also in the case of high-energy electron-electron as well as quark-quark scatterings. We present an exact combinatorial formula, involving multiple commutators of the vertices, which can be used to compute such cancelations. It is a non-abelian generalization of the eikonal formula, and will be applied in subsequent publications to study the consistency of large-Nc QCD involving baryons, as well as high-energy quark-quark scattering in ordinary QCD. (orig.)