By Julia Nyiri

V.N. Gribov, one of many founders of recent particle physics, formed our knowing of QCD because the microscopic dynamics of hadrons. This quantity collects his papers on quark confinement, displaying the line he to reach on the idea and formulating the idea itself. It starts with papers supplying a actual rationalization of asymptotic freedom in line with the phenomenon of anti-screening and demonstrating the inconsistency of the traditional perturbative therapy of the gluon fields (Gribov copies, Gribov horizon). It keeps with papers featuring the Gribov concept in accordance with which confinement of color depends upon the life of virtually massless quarks. The final papers finish Gribov's 20-year-long learn of the matter; QCD is formulated as a quantum box concept containing either perturbative and nonperturbative phenomena, and the confinement is predicated at the supercritical binding of sunshine quarks.

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**Extra resources for The Gribov Theory of Quark Confinement**

**Example text**

It is obvious that the solution, nonsingular for r -»• 0 (t —>• — x), corresponds to a pendulum which at t -*• —oo is in the position of unstable equilibrium a = 0 (or = rnr). When t —> — oo, we have a(t) -+ 7r —»• jel. (33) When t -> +oo, we have a(t) -> ± | , and, owing to the presence of the damping, for any t we get \a(t)\ < it. , it decreases as 1/r. 7(r), and consequently for B (r). is characterized by four parameters: three parameters T^o* which define the reference point, and a parameter 7, which has the meaning of an inverse radius of the region beyond which B\ decreases.

For the sake of simplicity we assume that *i,2n=ai,2*M+0i,2«n. (60) Let us now return to the integration which was performed when we derived (46). Multiplying (46) by x\[ J a ^r8ix\-2a'{xyz')-\ and interchanging the integrations over a' and Q\ we get 1 x\ f a'do' fd/2' , . n . » ^Ti~7rra ^ ~ 1 TTT^ -T—C^ZvSmFSip^-zz), 2-rr Xi(pi — p2) a J (ai —a +5) J 4-n- ] = £= ffi-g' «i« n r/3i. S = a/32- "2-Qi Pi-Pi At the choice of e according to (60) we have sin F(x, z') = sin F(z, —. z'). N. vz'v=*2a piz^, (ai==a2~a), • - lit "02 f a'da'p!

E.. ae ~ >/e. Then a ~ e2 also decreases with large r. As / further increases, e (the binding energy) increases, and the expansion in powers of e deteriorates. However, the solution still exists. When / increases to rhe point where a second level with a small binding energy e appears, then, by repeating the above operations, we shall show that a second solution appears. We therefore get a degree of ambiguity equal to the number of eigenvalues of the operator • . Actually, owing to the fact that a(oc) can equal not only zero but mr as well (the pendulum can sail through the equilibrium position several times from different directions), the degree of ambiguity of the fields B{ is even larger.