Möbius Representation for Reggeized Gluons

It is shown that the BFKL equation is invariant under a gauge-type transformation. As a result one can impose on the Pomeron wave function Ψ(ρ→1,ρ→2) the colour transparency condition Ψ(ρ→,ρ→)=0 valid for functions in the Möbius representation. The triple Pomeron vertex in the multi-colour QCD at this representation is equivalent to the integral kernel in the Balitiski-Kovchegov (BK) equation. As a result, the BK equation for the dipole density is obtained from the nonlinear equation for the sum of fan diagrams.