The Gribov Conception of Quantum Chromodynamics

A major contribution to the quest of constructing quantum dynamics of non-Abelian fieds is due to V.N. Gribov. Perturbative approach to the colour confinement, both in gluodynamics and the real world, was long considered heretic but is gaining ground. We discuss Gribov's approach to the confinement problem, centered around the role played by light quarks - the supercritical light quark confinement scenario. We also review some recent developments that are motivated, directly or indirectly, by his ideas.Comment: 60 pages, 6 figure

Confinement and the Pion Nucleon Sigma Term

Gribov's theory of confinement offers a simple explanaton of the value of the pion nucleon sigma term. There is no need to invoke a large strange quark component in the nucleon.Comment: 4 pages, Cavendish HEP 93/

Mass dependence of nuclear shadowing at small Bjorken-x from diffractive scattering

We calculate the nuclear shadowing ratio for a wide range of nuclei at small Bjorken-x in the framework of Gribov theory. The coherent contribution to the (virtual) photon-nucleon cross section is obtained in terms of the diffractive dissociation cross section. Information on diffraction from FNAL and HERA is used. Our results are compared to available experimental data from the NMC and E665 experiments at x ~ 10^{-4}.Comment: To be published in Phys. Rev.

Gribov's Confinement Scenario

I give a brief account of Gribov's scenario of supercritical charges in QCD. Gribov's equation for the Green function of light quarks and its derivation from the corresponding Dyson-Schwinger equation are described. The resulting Green function is shown to exhibit chiral symmetry breaking.Comment: 4 pages, 1 figure, Talk presented at the Xth International Light-Cone Meeting on Non-Perturbative QCD and Hadron Phenomenology, Heidelberg, June 200

QCD at large and short distances (annotated version)

The formulation of QCD which contains no divergences and no renormalization procedure is presented. It contains both perturbative and non-perturbative phenomena. It is shown that, due to its asymptotically free nature, the theory is not defined uniquely. The chiral symmetry breaking and the nature of the octet of pseudo-scalar particles as quasi-Goldstone states are analysed in the theory with massless and massive quarks. The U(1) problem is discussed. ======================================================================= Note: The original version of the paper completed by the author in April 1997 was submitted to the hep-ph archive (hep-ph/9708424) a few days after Prof. V.N. Gribov passed away on August 13, 1997. This is the first of the two papers concluding his 20 year long study of the problem of quark confinement in QCD. In an attempt to understand the paper by a group of his colleagues, started in November 1997 in Orsay, this annotated version appeared. A number of misprints were eliminated, most of the equations were checked, and some corrected. Comments have been added in order to make the text easier to read. These comments are displayed in square brackets. Many theorists participated in the process; the comments were assembled and the final version prepared by Yu. Dokshitzer, C. Ewerz, A. Kaidalov, A. Mueller, J. Nyiri and A. Vainshtein. The second paper ``The theory of quark confinement'' will soon be published.Comment: 38 pages, Latex, 108 figures included using epsfig.sty. Annotated version of hep-ph/9708424, misprints eliminated, equations checked and some corrected, comments added (see abstract for further details

Approximate Fitting of a Circular Arc When Two Points Are Known

The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of circular arcs fitting requires an efficient way of fitting circular arcs with complexity O(1). The elegant solution to this task based on an eigenvector problem for a square nonsymmetrical matrix is described in [1]. For the compression algorithm described in [2], it is necessary to solve this task when two points on the arc are known. This paper describes a different approach to efficiently fitting the arcs and solves the task when one or two points are known.Comment: 15 pages, 4 figures, extended abstract published at the conferenc

Ioffe Time in Double Logarithmic Approximation

We analyze the light cone (Ioffe) time structure of the gluon distribution function in the double logarithmic approximation. We show that due to QCD evolution Ioffe equation is modified. The characteristic light cone time of the gluons does not increase as fast with increasing energy (decreasing Bjorken x) as predicted by the parton distributions exhibiting Bjorken scaling due to the increase of the transverse momenta of the gluons in the DGLAP ladder.Comment: 13 pages, 1 figur