From loops to trees by-passing Feynman's theorem

Understand

We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts.

• The duality relation is realized 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 applied to generic one-loop quantities in any relativistic, local and unitary field theories.