A gauge invariant formulation of intrinsically nonperturbative QCD

Using a system of the corresponding Schwinger-Dyson equations of motion, a pure dynamical theory of quark confinement and spontaneous breakdown of chiral symmetry is formulated. It is based on dominated in the QCD vacuum self-interaction of massless gluons only, i.e., without involving some extra degrees of freedom. This interaction becomes strongly singular in the deep infrared domain leading thus to the enhancement of zero momentum modes in the nonperturbative QCD vacuum. Using theory of distributions, complemented by the dimensional regularization method, we have explicitly shown that strong infrared singularities can be put under control. In this way a new phase in QCD, intrinsically nonperturbative QCD which is manifestly gauge invariant, was discovered. As a result, a highly nontrivial dynamical and topological structure of the QCD vacuum has emerged within our approach. We have also explicitly shown how infrared multiplicative renormalization program should be done in order to self-consistently remove all the strong infrared singularities from the theory. The corresponding convergence conditions play a crucial role in this program. In this theory any physical observables are determined by such correlation functions from which all types of the perturbative contributions should be subtracted, by definition. Theory is not only infrared finite but it is free from the ultraviolet divergences as well. It has a mass gap $\Delta > 0$, i.e., there are no physical states in the interval $(0, \Delta)$. It explains confinement, spontaneous breakdown of chiral symmetry and other nonperturbative effects on a general ground and in self-consistent way.