The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniques

TL;DR

This paper introduces three innovative algorithms for symbolic multi-loop Feynman integral calculations, improving canonical form derivation, tensor reduction, and polynomial partial fractioning, enabling recent advances in quantum field theory computations.

Contribution

The paper presents new algorithms for canonical form derivation, tensor reduction, and polynomial partial fractioning in multi-loop calculations, enhancing computational efficiency and accuracy.

Findings

Algorithms successfully tested on real calculations

Facilitated recent novel results in multi-loop computations

Improved methods for symbolic Feynman integral analysis

Abstract

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate their identification. Second, we present a practical solution to the problem of multi-loop analytical tensor reduction. Finally, we discuss the partial fractioning of polynomials with external linear relations between the variables. All algorithms have been tested and used in real calculations.