  We argue that the exact gauge symmetry of the QCD Lagrangian does not
coincide with the symmetry of its ground state. The dynamical source of this
breakdown has been identified with the tadpole/seagull term, which renormalized
version called, the mass gap. It is explicitly present in the full gluon
self-energy. The true dynamical role of the mass gap was hidden in the QCD
ground state. To disclose it the splintering between the transverse conditions
for the full gluon self-energy and its subtracted counterpart has been derived.
We have established the equation of motion for the full gluon propagator on
account of the mass gap with a newly-derived generalized gauge. It is uniquely
fixed as a function of the gluon momentum. All this makes it possible to
present novel non-perturbative analytical approach to QCD, which we call the
mass gap approach. It allows to extend the mass gap concept to be accounted for
the QCD ground state as well. We have discovered the non-perturbative singular
solution for the full gluon propagator valid in the whole gluon momentum range,
while dominating at large distances (small gluon momenta) over all the other
possible solutions. It accommodates all the severe infrared singularities (when
the gluon momenta go to zero), which may appear in the QCD ground state due to
the self-interaction of massless gluon modes. We developed the theoretical
formalism how to put them under a firm mathematical control. Despite the exact
gauge symmetry is broken in the ground state, the renormalizability of the
theory is not affected. For this the 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).
