  We present a new formulation of the loop-tree duality theorem for higher loop
diagrams valid both for massless and massive cases. $l$-loop integrals are
expressed as weighted sum of trees obtained from cutting $l$ internal
propagators of the loop graph. In addition, the uncut propagators gain a
modified $i \delta$-prescription, named dual-propagators. In this new framework
one can go beyond graphs and calculate the integrand of loop amplitudes as a
weighted sum of tree graphs, which form a tree-like object. These objects can
be computed efficiently via recurrence relations.
