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Study of algorithm of Dirac algebra

狄拉克代数算法研究

基本信息

批准号：
10680366
负责人：
ISHIKAWA Tadashi
金额：
$ 1.09万
依托单位：
The High Energy Accelerator Research Organization
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680366/
关键词：
Divac algebra symbolic manipulation super-symmetry Loop calculation

项目摘要

We have developed GRACE system, an automatic computation system in particle physics. In this system, the expressions of Feynman amplitudes using Dirac algebra are eliminated in the symbolic manipulation way, and the numerical result of these expressions will be computed.In the symbolic manipulation package (REDUCE), the straightforward eliminations don't work due to lack of memory. After the study of algorithm of Dirac algebra, many complicated and sophisticated techniques have been introduced, so that the calculations of tree level and one-loop lever becomes reliable in the framework of standard model and super-symmetric model.Thus it is shown that these calculation will be successfully done. This fact means that 1-loop calculations will be automatically possible in principle. In order to check the symbolic calculation, two methods are studied and tested in the following way :・ Comparison with another symbolic manipulation had been done. In general,the expressions produced by REDUCE are quite different from those of another system (FORM). Then numerical comparison had been successfully done.・ The introduction of additional gauge parameters is very useful. The in-dependency of gauge parameter is found.Both methods are quite important to confirm the correctness of algorithm of symbolic manipulation, because the algorithm is rather complicated.Concerning the physical application, several processes in standard model and super-symmetric model are calculated.We should try the physical processes such a e+ e- → 4 fermion processes, which are important for the LEP-II experiment at CERN (European Organization for Nuclear Research).As the next step, the study of algorithm for helicity amplitude and the symbolical optimization should be considered to reduce the computation time for the symbolic step and numerical step.

我们开发了一个粒子物理自动计算系统GRACE。在该系统中，对狄拉克代数的费曼振幅表达式进行符号消元，并计算其数值结果，而在符号处理软件包REDUCE中，直接消元由于内存不足而无法实现。通过对Dirac代数算法的研究，引入了许多复杂而精细的技巧，使标准模型和超对称模型框架下的树级和单圈级的计算变得可靠，从而表明这些计算是可以成功完成的。这一事实意味着单循环计算在原则上将自动成为可能。为了检验符号运算，我们研究了两种方法，并通过以下方式进行了检验：·与另一种符号运算进行了比较。一般来说，REDUCE产生的表达式与另一个系统（FORM）的表达式有很大的不同。然后数值比较成功完成。·引入额外的规范参数是非常有用的。在物理应用方面，我们计算了标准模型和超对称模型中的几个过程，并尝试了e+ e- → 4费米子过程，在此基础上，我们还计算了几个物理过程，并给出了它们的计算结果，结果表明，这两种方法对于验证符号操作算法的正确性都是十分重要的，因为符号操作算法是相当复杂的。这些对于欧洲核子研究中心（CERN）的LEP-II实验非常重要，下一步应考虑研究螺旋度振幅算法和符号优化，以减少符号步骤和数值步骤的计算时间。