Iterated integrals over letters induced by quadratic forms

TL;DR

This paper develops automated methods for handling iterated integrals related to quadratic forms and Kummer--Poincaré letters, aiding calculations in Feynman diagram analysis.

Contribution

It introduces a systematic approach for reduction, expansion, analytic continuation, and numerical evaluation of these integrals, facilitating computer-algebraic applications.

Findings

Provides basis reduction techniques for iterated integrals

Enables analytic continuation of integral representations

Supports efficient numerical evaluation

Abstract

An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar\'e letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To compactify representations, one wishes to apply general properties of these quantities in computer-algebraic implementations. We provide the reduction to basis representations, expansions, analytic continuation and numerical evaluation of these quantities.