论文标题
与椭圆曲线相关的Feynman积分相关的迭代积分
Iterated integrals related to Feynman integrals associated to elliptic curves
论文作者
论文摘要
本演讲回顾了Feynman积分，这些积分与椭圆曲线相关。演讲将介绍其背后的数学，涵盖椭圆曲线，椭圆形积分，模块化形式和$ n $的模量空间的主题。后者将很重要，因为椭圆形的feynman积分可以用与Feynman积分相同的方式表示为模量空间$ {\ Mathcal m} _ {1，n} $，以评估对多个polylogarith的评估的方式相同，可以在多个polygarithms上表达为迭代积分，以迭代的迭代为单位，以迭代为$ {\ maths $ {\ math $ {\ m} nsect $ {\ m}。使用正确的语言，零病例中的许多方法都将属于属的情况。特别是在特定的示例中，我们将看到椭圆形Feynman积分的微分方程可以被施加到$ \ varepsilon $ -form中。这允许在维数正则化参数中系统地通过顺序获得解决方案。
This talk reviews Feynman integrals, which are associated to elliptic curves. The talk will give an introduction into the mathematics behind them, covering the topics of elliptic curves, elliptic integrals, modular forms and the moduli space of $n$ marked points on a genus one curve. The latter will be important, as elliptic Feynman integrals can be expressed as iterated integrals on the moduli space ${\mathcal M}_{1,n}$, in same way as Feynman integrals which evaluate to multiple polylogarithms can be expressed as iterated integrals on the moduli space ${\mathcal M}_{0,n}$. With the right language, many methods from the genus zero case carry over to the genus one case. In particular we will see in specific examples that the differential equation for elliptic Feynman integrals can be cast into an $\varepsilon$-form. This allows to systematically obtain a solution order by order in the dimensional regularisation parameter.
