Differential Equations for Definition and Evaluation of Feynman Integrals

TL;DR

This paper introduces a novel formalism that interprets Feynman integrals as Green functions of linear differential operators, simplifying calculations by avoiding regularization and R-operations.

Contribution

It presents a new approach to defining Feynman integrals through differential equations, eliminating the need for regularization and R-operations.

Findings

Feynman integrals can be represented as Green functions of differential operators.

The formalism simplifies practical calculations of Feynman integrals.

The approach is equivalent to traditional definitions but more convenient for computations.

Abstract

It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that presented formalism is convenient for practical calculations of Feynman integrals.