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.