A Refined Difference Field Theory for Symbolic Summation

TL;DR

This paper introduces a refined difference field theory that improves symbolic summation algorithms, enabling the derivation of sum representations with minimal nested depth, with applications in quantum field theory calculations.

Contribution

It presents a refined summation theory based on Karr's difference fields, enhancing the efficiency of symbolic summation algorithms for complex integrals.

Findings

Algorithms find sum representations with optimal nested depth

Successfully applied to evaluate Feynman integrals

Improves symbolic summation techniques in quantum physics

Abstract

In this article we present a refined summation theory based on Karr's difference field approach. The resulting algorithms find sum representations with optimal nested depth. For instance, the algorithms have been applied successively to evaluate Feynman integrals from Perturbative Quantum Field Theory.