Gauge invariant decomposition of 1-loop multiparticle scattering amplitudes

A simple algorithm is presented to decompose any 1-loop amplitude for scattering processes of the class 2 fermions→4 fermions into a fixed number of gauge-invariant form factors. The structure of the amplitude is simpler than in the conventional approaches and its numerical evaluation is made faster. The algorithm can be efficiently applied also to amplitudes with several thousands of Feynman diagrams.