  We derive a duality relation between one-loop integrals and phase-space
integrals emerging from them through single cuts. The duality relation is
realized by a modification of the customary +i0 prescription of the Feynman
propagators. The new prescription regularizing the propagators, which we write
in a Lorentz covariant form, compensates for the absence of multiple-cut
contributions that appear in the Feynman Tree Theorem. The duality relation can
be applied to generic one-loop quantities in any relativistic, local and
unitary field theories. %It is suitable for applications to the analytical
calculation of %one-loop scattering amplitudes, and to the numerical evaluation
of %cross-sections at next-to-leading order. We discuss in detail the duality
that relates one-loop and tree-level Green's functions. We comment on
applications to the analytical calculation of one-loop scattering amplitudes,
and to the numerical evaluation of cross-sections at next-to-leading order.
