The Mass Gap Approach to QCD. III. Solution of the gluon confinement problem

We present reports on progress in the solution of the gluon confinement problem and in the explanation of the scale breaking in the asymptotic freedom regime in QCD. It is based on the previously formulated the mass gap approach to QCD, which sheds the light on a mass origin in its ground state. We have established the exact expression for the full gluon propagator. One of its solution allows to sum up all the severe (more singular than 1/q²) infrared singularities which can be accommodated by a single full gluon propagator. In order to correctly treat them, we have developed a formalism of the joint use of the theory of functions of complex variable, and the dimensional regularization method correctly implemented into the theory of distributions. Despite the presence of the mass gap, gluons remain massless. Our solution satisfies the two boundary conditions: it dominates over all other possible solutions at large distances but itself prevents gluons to appear in the physical spectrum. It possesses the asymptotic freedom behaviour at short distances. We discuss the connection of our results to the Elitzur's theorem.