  The calculation of scattering amplitudes in Yang-Mills theory at loop level
is important for the analysis of background processes at particle colliders as
well as our understanding of perturbation theory at the quantum level. We
present tools to derive relations for especially one loop amplitudes, as well
as several explicit examples for gauge theory coupled to a wide variety of
matter. These tools originate in certain scaling behavior of permutation and
cyclic sums of Yang-Mills tree amplitudes and loop integrands. In the latter
case evidence exists for relations at all loop orders.
