46 research outputs found
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 -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 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.
A Nonperturbative Calculation of Basic Chiral QCD Parameters Within Zero Modes Enhancement Model of the QCD Vacuum. I
A new zero modes enhancement (ZME) model of the true QCD vacuum is breifly
described. It makes possible to analytically investigate and calculate
numerically low-energy QCD structure from first principles. Expressions of
basic chiral QCD parameters (the pion decay constant, the quark and gluon
condensates, the dynamically generated quark mass, etc) as well as the vacuum
energy density (up to the sign, by definition, the bag constant), suitable for
numerical calculations, have been derived. Solution to the Schwinger-Dyson (SD)
equation for the quark propagator in the infrared (IR) domain on the basis of
the ZME effect in QCD was used for this purpose. There are only two independent
quantities (free parameters) by means of which calculations must be done within
our approach. The first one is the integration constant of the above mentioned
quark SD equation of motion. The second one is a scale at which nonperturbative
effects begin to play a dominant role.Comment: 17 pages, two figures added, minor change
Gluon confinement criterion in QCD
We fix 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 ) infrared singularities. It reflects
the zero momentum modes enhancement effect in the true QCD vacuum, which is due
to the self-interaction of massless gluons. It existence automatically exhibits
a characteristic mass (the so-called mass gap). It is responsible for the scale
of nonperturbative dynamics in the true QCD ground state. The theory of
distributions, complemented by the dimensional regularization method, allows
one to put the severe infrared singularities under the 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 . Thus we have exactly
established the interaction between quarks (concerning its pure gluon (i.e.,
nonlinear) contribution) up to its unimportant perturbative part. This also
makes it possible for the first time to formulate the gluon confinement
criterion and intrinsically nonperturbative phase in QCD in a manifestly
gauge-invariant ways.Comment: 10 pages, no figures, no tables. Typos corrected and the
clarification is intoduced. Shorten version to appear in Phys. Lett.