Causality and loop-tree duality at higher loops

Abstract

We relate a $l$-loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original $l$-loop graph. Causality requires that the propagators of the trees have a modified $i\delta$-prescription and we present a simple formula for the correct $i\delta$-prescription.

Comments: 6 pages, v2: version to be published, v3: Theorem 1 corrected