Structure of the Yang-Mills vacuum in the zero modes enhancement quantum model

We have formulated new quantum model of the QCD vacuum using the effective potential approach for composite operators. It is based on the existence and importance of such kind of the nonperturbative, topologically nontrivial excitations of gluon field configurations, which can be effectively correctly described by the $q^{-4}$-type behavior of the full gluon propagator in the deep infrared domain. The ultraviolet part of the full gluon propagator was approximated by the asymptotic freedom to-leading order perturbative logarithm term of the running coupling constant. Despite the vacuum energy density remains badly divergent, we have formulated a method how to establish a finite (in the ultraviolet limit) relation between the two scale parameters of our model. We have expressed the asymptotic scale parameter as $pure number$ times the nonperturbative scale, which is inevitably contained in any realistic Ansatz for the full gluon propagator.Comment: 16 pages, no figures, no tables, to appear in Phys. Lett.

Vacuum instability in the Abelian Higgs model with strings

Using the effective potential approach for composite operators, we have analytically evaluated the truly nonperturbative vacuum energy density in the Abelian Higgs model of dual QCD ground state. This quantity is defined as integrating out of the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). Defined in this way it is manifestly gauge invariant.We have explicitly shown that the corresponding effective potential always has an imaginary part. This means that the vacuum of this model with string contributions is unstable against quantum corrections.Comment: 7 pages, no tables, no figures. Some clarifications are introduced as well as two more references have been added. To appear in Phys. Lett.

How to explicitly introduce the Jaffe-Witten mass gap into the quantum Yang-Mills theory

We propose how to explicitly introduce the Jaffe-Witten mass gap into the quantum Yang-Mills theory. Through the full gluon propagator it is defined as such nonperturbative scale that when it formally goes to zero, then the perturbative phase survives in the theory only. The close link between mass gap and strong infrared singularities which are due to dominated in the QCD vacuum self-interaction of massless gluons is also discussed. This interaction leads thus to the zero momentum modes enhancement effect in the QCD nonperturbative vacuum. Using theory of distributions, we argue that strong nonperturbative infrared singularities can be put under control. A new, intrinsically nonperturbative phase in QCD is established.Comment: Talk given at Sixth Workshop on Non-Perturbative Quantum Chromodynamics, 5-9 June 2001, Paris, Franc