Effective locality and gauge invariance

A few years ago, based on standard functional manipulations, an unexpected property was proven to be satisfied by the fermionic Green's functions of QCD, and dubbed effective locality. This feature of QCD is non-perturbative as it results from a full integration of the fermionic and gluonic degrees of freedom. Previous derivations of effective locality are reviewed, corrected, and enlarged. Focussing on the way non-abelian gauge invariance is realized in the non-perturbative regime of QCD, the meaning of effective locality is proposed.