β Scribed by A.A Migdal
No coin nor oath required. For personal study only.
The system of equations of motion for the n-loop averages in QCD are derived and investigated in detail. A gauge and Lorentz invariant regularization is proposed. A closed equation is obtained for the one loop average at an infinite number of colors with fixed ratio to the number of flavors.
Quantum chromodynamics (CDC) cannot be considered as a complete theory. Although it looks reasonable at the phenomenological level, the essential ingredients of the microscopic theory are still missing.
The perturbative formulation, even after incorporation of instantons, does not describe the confining phase. The meron-like configurations are more relevant, but there is no systematic way to take them into account. The lattice formulation by Wilson or Kogut and Susskind would serve as a microscopic definition of QCD, were it not for the spurious phase transitions which are likely to occur in lattice gauge theories. One can never be sure that the strong coupling expansion of the given lattice theory describes asymptotically free QCD.
From the pragmatic point of view the problem is to find a reasonable zeroth approximation to QCD in a confining phase, and to develop the corresponding perturbation theory. Such an approach, the l/N expansion, was proposed by 't Hooft [I] and developed by Veneziano; Koplik, Neveu, and Nussinov; Brezin, Itzyckson, Parisi, and Zuber; Thorn [2]; as well as by Migdal [3] and others.
In two dimensions the terms of the l/N expansion are calculable and the dual theory that arises looks quite nice. That much was done in the general case. The topological analysis of the diagrams indicates that the l/N expansion should correspond to a certain dual resonance theory with the dual coupling constant -N-l. The leading "Born" term corresponds to the sum of all the planar diagrams. Once the Born term is found, the l/N corrections can in principle be found by unitarization, as in conventional dual theories.
In a recent paper by Makeenko and the author [4] a closed equation was obtained for the one-loop average at N = co. This equation generates all planar diagrams. The present paper consists of several parts. In Sections II and III we derive the quantum equations of motion for the n-loop averages. The investigation of these equations of 279
π SIMILAR VOLUMES
We study some structural aspects of the evolution equations with pomeron loops recently derived in QCD at high energy and for a large number of colors, with the purpose of clarifying their probabilistic interpretation. We show that, in spite of their appealing dipolar structure and of the self-duali