Observing new physics at hadron colliders requires a detailed description of multi-particle scattering events. It is not practical to evaluate Feynman diagrams directly for all significant processes. Moreover, adding all diagrams reveals many cancellations, ending in surprisingly simple formulas. I will present new methods to get QCD amplitudes compactly and efficiently, preserving gauge invariance at every step. Tree amplitudes appear directly in their shortest forms from recursion relations. Loop momentum integration is replaced by a sequence of algebraic operations.

Amsterdam