Automatic calculation of Feynman amplitudes

本研究项目的目标是开发一个用于计算标准模式中的辐射改正的自动化系统。在1993-1995年项目方面，取得了以下进展。开发了一个用于计算一般质量和动量情况下的单圈积分的数值计算库。在质量壳方案的基础上，给出了重整化的反义项。对于两对二相互作用的几个样本，如e^+e^-*HZ，e^+e^-*TT，Gamma*TT，完成了自动计算，并通过几个校核过程验证了其准确性。引入了一种额外的处理来确定Gamma矩阵的顺序，使得对于一类具有Gamma_5的幅值来说，可能的模糊性是无害的。这一点在e^+e^-*W^+W^-4的计算中得到了明确的证明。发展了一种计算一般质量和动量的两圈标量两点函数和三点函数的数值方法。作为双环自动化的一个例子，用弱电理论计算了Mu的反常磁矩。已有部分结果证明了该方法的有效性。

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.