True Dynamical and Gauge Structures of the QCD Ground State and the Singular Gluon Fileds

We convincingly argue that the true dynamical and gauge structure of the QCD ground state is much more complicated than its Lagrangian exact gauge symmetry supposes to be. The dynamical source of these complications has been identified with the tadpole/seagull term, which renormalized version called, the mass gap. Its true dynamical role is hidden in the QCD ground state, but it is explicitly present in the full gluon self-energy. To disclose it the splintering between the transverse conditions for the full gluon self-energy and its subtracted counterpart has been derived. The equation of motion for the full gluon propagator on account of the mass gap was given, which allows to fix the dynamical and gauge structures by a newly-introduced generalized gauge. A novel non-perturbative analytical method, the mass gap approach was developed for QCD and its groud state as well. We have discovered a general, non-perturbative singular solution for the full gluon propagator valid in the whole gluon momentum range, while dominating at large distances over all the other possible solutions. It accommodates all the severe infrared singularities, which may appear in the QCD ground state due to the self-interaction of massless gluon modes. A corresponding non-pertubative multiplicative infrared renormalization program has been formulated. The resulting full gluon propagator prevents gluons to appear at large distances as physical states (confinement of color gluons). Our approach also explains the scale violation in the asymptotic freedom regime, and why the rising potential between heavy quarks is only linear one.