Connection between complete and Moebius forms of gauge invariant operators

TL;DR

This paper explores the relationship between complete and Moebius forms of gauge invariant operators, demonstrating how to reconstruct complete representations from Moebius forms and providing explicit operators for kernel transitions.

Contribution

It introduces a method to restore complete gauge invariant operators from their Moebius forms and derives operators for transitioning between BFKL kernels.

Findings

Restoration method for complete representations from Moebius forms

Explicit operators for BFKL kernel transition

Proof of reconstructing complete operators in coordinate space

Abstract

We study the connection between complete representations of gauge invariant operators and their Moebius representations acting in a limited space of functions. The possibility to restore the complete representations from Moebius forms in the coordinate space is proven and a method of restoration is worked out. The operators for transition from the standard BFKL kernel to the quasi-conformal one are found both in Moebius and total representations.