Intrinsically nonperturbative QCD I. A pure dynamical theory of gluon confinement

We establish exactly and uniquely the infrared structure of the full gluon propagator in QCD, not solving explicitly the corresponding dynamical equation of motion. By construction, this structure is an infinite sum over all possible severe (i.e., more singular than $1/q^2$) infrared singularities. It reflects the zero momentum modes enhancement effect in the true QCD vacuum. Its existence exhibits a characteristic mass (the so-called mass gap), which is responsible for the scale of nonperturbative dynamics in the QCD ground state. The theory of distributions, complemented by the dimensional regularization method, allows one to put severe infrared singularities under firm mathematical control. By an infrared renormalization of a mass gap only, the infrared structure of the full gluon propagator is exactly reduced to the simplest severe infrared singularity, the famous $(q^2)^{-2}$. So, the smooth in the infrared limit the full gluon propagator is to be ruled out. Collective motion of all the purely transverse $virtual$ gluon field configurations with low-frequency components/large scale amplitudes is solely responsible for the color confinement phenomenon within our approach. At the microscopic, dynamical level these field configurations are saturated by the nonlinear fundamental four-gluon interaction. It just makes the full gluon propagator inevitably so singular in the infrared. The amplitudes of all the purely transversre severely singular $actual$ gluon field configurations are totally suppressed, leading thus to the confinement of gluons. We formulate exactly the gluon confinement criterion in a manifestly gauge-invariant way, taking into account the distribution nature of severe infrared singularities.