From multileg loops to trees (by-passing Feynman's Tree Theorem)

TL;DR

This paper introduces a duality relation linking one-loop integrals to single-cut phase-space integrals through a modified Feynman prescription, simplifying calculations in quantum field theory.

Contribution

It presents a novel duality relation that bypasses the need for multiple cuts in Feynman diagrams by modifying the propagator prescription, applicable to various one-loop quantities.

Findings

Duality relation expressed via a Lorentz covariant prescription

Regularizes propagators to avoid multiple-cut contributions

Applicable to Green's functions in relativistic field theories

Abstract

We illustrate a duality relation between one-loop integrals and single-cut phase-space integrals. The duality relation is realised by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple-cut contributions that appear in the Feynman Tree Theorem. The duality relation can be extended to generic one-loop quantities, such as Green's functions, in any relativistic, local and unitary field theories.