  Using loop-tree duality, we relate a renormalised $n$-point $l$-loop
amplitude in a quantum field theory to a phase-space integral of a regularised
$l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like
object. We show that up to three loops the latter object is easily computable
from recurrence relations. This defines an integrand of the loop amplitude with
a global definition of the loop momenta. Field and mass renormalisation are
performed in the on-shell scheme.
