| Project/Area Number |
10640285
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
素粒子・核・宇宙線
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| Research Institution | Meiji Gakuin University |
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Principal Investigator |
KANEKO Toshiaki Meijigakuin University, Department of Low, Professor, 法学部, 教授 (40177522)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIKAWA Tadashi High Energy Accelerator Research Organization, Assistant Professor, 計算科学センター, 助教授 (90184481)
KURODA Masaaki Meijigakuin University, Department of Low, Professor, 法学部, 教授 (00170134)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2000: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | automatic calculation / Feynman amplitudes / Super symmetry / MSSM / Feynman rules / Non-linear gauge / Computer algebra / Lagrangian / GRACE / SUSY / 自動計算 / 数式処理 / 摂動論 |
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| Research Abstract |
We have been developing an automatic calculating system of Feynman amplitudes grace. In this Study, we have extended this system for Majorana particles and vertices in which Fermion numbers do not conserve. With a file describing Feynman rules of MSSM, grace system automatizes the whole proeess from the generation of Feynman graphs to the calculation of scattering cross sections and the generation of simulated events.
We have also extended the system for 1 loop processes in both standard model and MSSM. For standard model, calculation in non-linear gauge is available, with which one can numerically confirm the gauge invariance of the obtained results.
In MSSM, we have 86 particles, 3803 tree vertices and counter terms. We wrote them down in a machine readable form and we have checked gauge invariance for all possible processes with 6 external particles in order to confirm the correctness of the input Feynman rules. This procedure requires a large amount of man power and computer resources. It is not easy task to introduce such a complicated models by hand and is necessary to introduce a system which derive Feymnan rules from arbitral Lagrangian.
We have started to develop special purpose symbolic manipulating system. Since a Lagrangian includes wide varieties of mathematical objects, we are developing it as an interpreter of a newly designed computer programming language. It includes as usual computer programming language, functions of control structures, sub-program and composite data structures such as lists, arrays and records. It also manipulates rational numbers of arbitrary precision, mathematical symbols and symbolic mathematical operations. At this moment, we can derive Feynman rules automatically for QED with this system.
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