Scattering amplitudes from a deconstruction of Feynman diagrams

We show how to apply the BCFW recursion relation to Feynman loop integrals with the help of the Feynman-tree theorem. We deconstruct in this way all Feynman diagrams in terms of on-shell subamplitudes. Every cut originating from the Feynman-tree theorem corresponds to an integration over the phase space of an unobserved particle pair. We argue that we can calculate scattering amplitudes alternatively by the construction of on-shell and gauge-invariant subamplitudes.