论文标题
椭圆形的模块化转换
Modular transformations of elliptic Feynman integrals
论文作者
论文摘要
我们研究了模块化转换下椭圆形Feynman积分的行为。这有一个实用的动机：通过合适的模块化转换，我们可以实现nome平方是少量的，从而导致快速的数值评估。与多种聚类的情况相反，仅考虑多个多聚群的数值评估的可变变换就足够了，在椭圆形的情况下，考虑变量转换（即模块化转换）的组合以及对主体积分的重新定义，它更自然。因此，我们将基础歧管上的坐标转换与纤维中的基础转换结合在一起。只有在两种转换的结合中，我们才保持在同一类函数中。
We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast numerical evaluations. Contrary to the case of multiple polylogarithms, where it is sufficient to consider just variable transformations for the numerical evaluations of multiple polylogarithms, it is more natural in the elliptic case to consider a combination of a variable transformation (i.e. a modular transformation) together with a redefinition of the master integrals. Thus we combine a coordinate transformation on the base manifold with a basis transformation in the fibre. Only in the combination of the two transformations we stay within the same class of functions.
