  Recently, it has been shown that on-shell scattering amplitudes can be
constructed by the Feynman-tree theorem combined with the BCFW recursion
relations. Since the BCFW relations are restricted to tree diagrams, the
preceding application of the Feynman-tree theorem is essential. In this way
amplitudes can be constructed by on-shell and gauge-invariant tree amplitudes.
Here we want to apply this method to the electron-photon vertex correction. We
present all the single, double, and triple phase-space tensor integrals
explicitly and show that the sum of amplitudes coincides with the result of the
conventional calculation of a virtual loop correction.
