Derivation of Functional Equations for Feynman Integrals from Algebraic Relations

TL;DR

This paper introduces new algebraic methods to derive functional equations for Feynman integrals, enabling their expression in terms of simpler integrals across various kinematic configurations.

Contribution

The paper presents novel algebraic techniques for deriving functional equations for Feynman integrals, applicable to one- and two-loop cases, facilitating their simplification.

Findings

Functional equations for various integrals are derived.

Feynman integrals can be expressed in terms of simpler integrals.

Methods are applicable to general kinematic conditions.

Abstract

New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of functional equations Feynman integrals in general kinematics can be expressed in terms of simpler integrals.