Causality and Loop-Tree Duality at Higher Loops
Robert Runkel (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany); Zoltán Szőr (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany); Juan Pablo Vesga (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany); Stefan Weinzierl (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany)
We relate an -loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original -loop graph. Causality requires that the propagators of the trees have a modified prescription, and we present a simple formula for the correct prescription.