The five-twist identity for Feynman periods

TL;DR

This paper introduces a new mathematical identity for Feynman periods related to five-vertex cuts, expanding the toolkit for analyzing quantum field theory integrals beyond existing identities.

Contribution

It presents a novel five-twist identity for Feynman periods that is independent of known identities like the twist and Fourier identities in $\,phi^4$ theory.

Findings

The five-twist identity applies to five-vertex cuts of primitive Feynman graphs.

It is independent from existing identities such as the twist and Fourier identities.

The identity enhances understanding of Feynman periods in quantum field theory.

Abstract

We prove a new identity for Feynman periods that acts on five-vertex cuts of completed primitive Feynman graphs. It is shown that in $\phi^4$ theory this identity is independent from existing identities which are the twist, the Fourier identity and the Fourier split.