Factorization of tree Feynman amplitudes

An algorithm is proposed to accelerate the calculation of tree processes by classifying Feynman graphs and factorizing Feynman amplitudes. Feynman graphs in a process are classified without duplication based on graph theoretical consideration. The classification and factorization method are applied recursively without generating Feynman graphs explicitly. Calculations in Electro-weak theory became 10–100 times faster than the traditional method for processes with six or seven final particles.