Soft gluon cascades and BFKL equation

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In this paper we deal with high energy scattering in the Regge limit, using a soft cascade approach. We derive an evolution equation for the gluon density in soft gluons cascades in the leading logarithmic approximation of perturbative QCD, and show that this equation reproduces BFKL equation in the forward case. The whole cascade is equivalent to a single gluon whose self-energy is responsible for gluon reggeization. The same type of equation is obtained for the QED case.
completely revised and rewritten version, 19 pages, latex file, 6 figures using feynman package

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