The Gribov Conception of Quantum Chromodynamics

We review lattice evidence showing that center-vortex condensation is a serious candidate for the mechanism of colour confinement in quantum chromodynamics.

In this paper we construct a wide class of Gribov copies in Coulomb gauge SU(2) gauge theory. Infinitesimal copies are studied in some detail and their non-perturbative nature is made manifest. As an application it is shown that the copies prevent a non-perturbative definition of colour charge.

The recent development of the Field Correlator Method (FCM) is discussed, with applications to the most interesting areas of QCD physics obtained in the lattice data and experiment. These areas include: a) the connection of colorelectric confinement with the basic quark and gluon condensates; b) the explicit form of the colorelectric deconfinement at a growing temperature $T$; c) the theory of the colormagnetic confinement at all temperatures; d) the theory of strong decays, ...

Recent progress done in Pisa on the subject is presented. It is shown that dual superconductivity of the vacuum or absence of it is an intrinsic property of QCD vacuum, independent of the choice of the abelian projection. The order of the deconfining phase transition in $N_f=2$ QCD is studied as a key to understand the mechanism of confinement.

In this paper we solved the new evolution equation for high energy scattering amplitudethat stems from the Gribov-Zwanziger approach to the confinement of quarks and gluons. We found that (1) the energy dependence of the scattering amplitude turns out to be the same as for QCD BFKL evolution; (2) the spectrum of the new equation does not depend on the details of the Gribov-Zwanzinger approach and (3) all eigenfunctions coincide with the eigenfunctions of the QCD BFKL equation...

I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribov's confinement scenario is realized in this gauge. For this purpose I will discuss in detail the emergence of the horizon condition and the Coulomb string tension. I will show that both are induced by center vortex gauge field configurations, which establish the connection between Gribov's confinement scenario and the center vortex picture of confinement. I will then extend...

We study nonperturbative features of QCD using the dual Ginzburg-Landau theory. The color confinement is realized through the dual Higgs mechanism, which is brought by QCD-monopole condensation. We investigate the infrared screening effect on the color confinement due to the light-quark pair creation. By solving the Schwinger-Dyson equation, we find that the dynamical chiral-symmetry breaking is largely brought by the confining force.

The status of the theory of color confinemnt is discussed.

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 s...

An attempt is made to describe from first principles the large-scale structure of the confining vacuum in quantum chromodynamics. Starting from our previous variational studies of the SU(2) pure gauge theory in an external Abelian chromomagnetic field and extending the Feynman's qualitative analysis in (2+1)-dimensional SU(2) gauge theory, we show that the SU(3) vacuum in three-space and one-time dimensions behaves like a disordered chromomagnetic condensate. Color confinemen...