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

Understand

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.