Light-like Wilson line in QCD without path ordering

Unlike the Wilson line in QED, the Wilson line in QCD contains path ordering. In this paper, we get rid of the path ordering in the light-like Wilson line in QCD by simplifying all the infinite number of noncommuting terms in the SU(3) pure gauge. We prove that the light-like Wilson line in QCD naturally emerges when path integral formulation of QCD is used to prove factorization of the soft and collinear divergences at all orders in coupling constant in QCD processes at high-energy colliders.