Feynman amplitudes automatic computation and its application

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In the years 1992 and 1993, it has been reported that the GRACE system has been developed and we made documentations, comparison to other systems, application to a few physical processes. Main results of the project in 1995 are as follows :1.The graph generator for any order of amplitude is developed. The generation can be done efficiently based on the method in graph theory.2.Standard mappings for kinematics are installed in the GRACE system to be chosen by the user.3.The graphical user interface of GRACE system is improved, so that the user can specify the conditions and parameters interactively.4.Through the collaborating work between Japan and France, the connection to the PAW system developed by CERN is included in GRACE system. In result, the control of system and the display of the computation can be done in an unified environment.5.Systematic study of tree amplitudes is done. We have studied most of the important processes with final 3-body states which can be expected in the f … More uture electronpositron collider. The result is open as a format of catalog.6.For the automatic computation of one-loop amplitudes, the processes e^+e^-*tt^^- and gammagamma*tt^^- are studied.7.A method to simplify the lengthy expression of generated code for amplitudes is developed.8.Improvement of numerical integration is done to adapt the parallel computing. Using super computer VPP500, the complete computation of a five-body process, e^+e^-*e^-v^^-_eud^^-gamma, can be executed.9.The extension of system to include the supersymmetric theory is done by the upgrade of CHANEL library so that it includes Majorana particles.10.We elaborate an effective lagrangian of charged-current and neutral current electroweak interaction which contains three free parameters. The physical meaning of these parameters and the experimental value of these parameters extracted from LEP1 data are discussed on connections with the possible physics beyond the standard model.In conclusion, the expert system important for high-energy physics has been evolving in this project. Less