📝 SummarXiv

Abstract

DGLAP integro-differential equation can be solved by applying certain map in the complex plane of Mellin moments. It may be re-written as Schr\"odinger equation for $n$ particles. By applying another map in the complex plane of Mellin moment we may re-write the DGLAP equation as a dual DGLAP equation. Regge limit of the dual DGLAP equation coincides with BFKL integro-differential equation which in turn is the Regge limit of optic theorem in quantum field theory and may be re-written as another Schr\"odinger equation. This means that the BFKL equation and the corresponding Schr\"odinger equation may be solved by the proposed method of complex mapping in the complex plane of Mellin moments. This approach may be useful in solving tasks related to quantum communication processes.