Iterated integrals in Feynman integral computations

费曼积分计算中的迭代积分

• 批准号: 270958718
• 负责人: Dr. Christian Bogner
• 金额: --
• 依托单位: Institut für Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/270958718?language=en
• 关键词: Iterated; integrals; Feynman; integral; computations

The computation of Feynman integrals is crucial for theoretical predictions at modern particle colliders. Powerful computational methods exist for Feynman integrals which can be expressed in terms of multiple polylogarithms or related generalizations of classical polylogarithms. One focus of this project is the improvement and further automatization of two of these techniques by use of a certain class of iterated integrals which represents the multiple polylogarithms and which has particularly good properties for the practical use in such computations. With the help of concrete algorithms and their implementation for the symbolical computation with this very general class of functions, we attempt the improvement of the derivation of Feynman integrals via direct parametric integration and via the expansion of hypergeometric functions.A second focus of the project is a subset of Feynman integrals, which according to the present state of the art cannot be expressed in terms of multiple polylogarithms. Computational methods which rely on the use of iterated integrals cannot be applied to these cases so far. Recent progress suggests that elliptic polylogarithms are an appropriate class of functions for the computation of such Feynman integrals. In this project we explore the further use and strive for an establishment of elliptic polylogarithms in Feynman integral computations. The possibility of expressing elliptic polylogarithms in terms of iterated integrals may lead to the development of a first systematic method for this problematic class of Feynman integrals.

费曼积分的计算对于现代粒子对撞机的理论预测至关重要。强大的计算方法存在的费曼积分，可以表示在多个多项式或相关的推广的经典多项式。该项目的一个重点是改进和进一步自动化的两个这些技术的使用的某一类迭代积分，代表了多个polygonms，并具有特别好的性能，在这种计算中的实际使用。借助这类函数的符号计算的具体算法和实现，我们尝试通过直接参数积分和超几何函数的展开来改进Feynman积分的推导。第二个重点是Feynman积分的一个子集，根据目前的技术水平，它不能用多重多项式表示。到目前为止，依赖于使用迭代积分的计算方法不能应用于这些情况。最近的进展表明，椭圆多项式是一个适当的一类功能的计算这样的费曼积分。在本项目中，我们探索椭圆多对数在费曼积分计算中的进一步使用并努力建立椭圆多对数。用迭代积分表示椭圆多项式的可能性可能会导致费曼积分这类问题的第一个系统方法的发展。