We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its application to two- and three-loop scalar master integrals and discuss the structure of the occurring cuts.
@article{arxiv.1011.0585,
title = {Feynman's Tree Theorem and Loop-Tree Dualities},
author = {Isabella Bierenbaum and Stefano Catani and Petros Draggiotis and German Rodrigo},
journal= {arXiv preprint arXiv:1011.0585},
year = {2010}
}