Iterated integrals in Feynman integral computations

• Applicant: Dr. Christian Bogner
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2015 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 270958718

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.

• DFG Programme: Research Grants