Automatic calculation of Feynman amplitudes

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The goal of this research project is to develop an automated system for the calculation of radiative corrections in the standard model. In the term of project, 1993-1995, the following progress is achieved.1. A library for the numerical computation is developed to calculate one-loop integrals for the case of general masses and momenta. The counter terms for the renormalization are also prepared based on the on-mass-shell scheme.2. For a few sample of two-to-two interactions, e.g., e^+e^-*HZ, e^+e^-*tt, gammagamma*tt, the automatic computation is done and it is verified to be exact through a few checking processes.3. An extra treatment to fix the ordering of gamma matrices is introduced, so that the possible ambiguity becomes harmless for a class of amplitudes with gamma_5. This is explicitly demonstrated in the calculation of e^+e^-*W^+W^-.4. A numerical method is developed to calculate the two-loop scalar two- and three-point functions for the general masses and momenta.5. As an example of automation in two-loop, the anomalous magnetic moment of mu is calculated in two-loop order of electro-weak theory. A part of result is already available to prove the validity of the method.