The Mass Gap Approach to QCD. II. The non-perturbative renormalization theory for the massive gluon fields

Abstract

The previously formulated the mass gap approach to QCD, based on a new insights into its ground state(vacuum), makes it possible to exactly define the dynamically generated gluon pole mass. We developed a non-perturbative multiplicative renormalization program for the corresponding massive full gluon propagator. Its asymptotic properties have been analyzed, including the perturbation theory limit to the free gluon state, i.e., no asymptotic freedom effect. The peculiarities of the mass-shell structure of the massive full gluon propagator has been discussed. The inconsistency of the canonical gauge in QCD is fixed. Our approach does not allow the massive gluons to be mass-shell objects. This prevents them to appear in the physical spectrum (confinement of the massive gluon states). The massive gluons may exist in the vacuum or inside hadrons only. Expression for massive full gluon propagator in Euclidean metric for the lattice simulations is present. It is also shown that the massive solution has a correct limit to the massless full gluon propagator, when the gluon pole mass is to be formally put zero.

Comments: 21 pages, no figures. A lot of new clarifying sentences, changes and corrections have been introduced. Due to these multiplying changes for the replacement version primary hep-th and cross-list to hep-lat categories will be more adequate to use