Abstract:
In my talk, I will discuss the success of applying the operator formalism to the calculation of massless Feynman diagrams. I will touch on the basics of this method, and then demonstrate how this approach helped to obtain a proof of the Broadhurst-Kreimer conjecture about the values of zig-zag multiloop diagrams which make a significant contribution to the renormalization group β-function in the 4-dimensional φ4 quantum field theory. The main part of the talk will be devoted to the construction of the so-called graph-building operator and the use of its conformal properties for its diagonalization.
The talk is based on https://arxiv.org/abs/2201.12232 and https://arxiv.org/abs/2302.11238.