Schroedinger泛函中Feynman规则的自动生成
Automatic generation of Feynman rules in the Schroedinger functional
摘要：
我们提供了一个算法，以产生顶点的薛定谔功能与阿贝尔背景规范场。背景场具有非平凡的颜色结构，因此我们主要关注颜色矩阵部分的操作。我们提出了如何实现该算法，特别是在Python代码。通过使用代码产生的python输出，我们还展示了如何将时间-动量以及坐标空间中的顶点的数值表达式写入费曼图计算代码。作为算法应用的例子，我们给出了一些单圈结果，格形规范作用量与由六个环（矩形环、椅形环和椭圆形环）组成的改进规范作用量的λ参数之比，O（a）边界反项的确定，以及Schroedinger泛函耦合常数的阶跃标度函数的微扰截止效应.
英文摘要：
We provide an algorithm to generate vertices for the Schrödinger functional with an abelian background gauge field. The background field has a non-trivial color structure, therefore we mainly focus on a manipulation of the color matrix part. We propose how to implement the algorithm especially in python code. By using python outputs produced by the code, we also show how to write a numerical expression of vertices in the time-momentum as well as the coordinate space into a Feynman diagram calculation code. As examples of the applications of the algorithm, we provide some one-loop results, ratios of the Lambda parameters between the plaquette gauge action and the improved gauge actions composed from six-link loops (rectangular, chair and parallelogram), the determination of the O(a) boundary counter term to this order, and the perturbative cutoff effects of the step scaling function of the Schroedinger functional coupling constant.
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