Overlapping-divergence-free skeleton expansion in non-Abelian gauge theories

We derive a skeleton expansion in Yang-Mills theory, which is completely free of overlapping divergences. This skeleton expansion provides a generalization of the Schwinger-Dyson equations of quantum electrodynamics to non-Abelian gauge theories. It yields a simple procedure for calculating renormalized perturbation theory integrals without using regulators and could serve as a starting point for nonperturbative approximations. In carrying out this analysis, we show that the Yang-Mills vector self-energy function and the Yang-Mills vector three-point function are uniquely determined by the Ward-Takahashi identity in terms of the other three basic vertex functions.