  We investigate relations between loop and tree amplitudes in quantum field
theory that involve putting on-shell some loop propagators. This generalizes
the so-called Feynman tree theorem which is satisfied at 1-loop. Exploiting
retarded boundary conditions, we give a generalization to L-loop expressing the
loops as integrals over the on-shell phase space of exactly L particles. We
argue that the corresponding integrand for L>2 does not involve the forward
limit of any physical tree amplitude, except in planar gauge theories. In that
case we explicitly construct the relevant physical amplitude. Beyond the planar
limit, abandoning direct integral representations, we propose that loops
continue to be determined implicitly by the forward limit of physical connected
trees, and we formulate a precise conjecture along this line. Finally, we set
up technology to compute forward amplitudes in supersymmetric theories, in
which specific simplifications occur.
