On the Method of Brackets: Rules, Examples, Interpretations and Modifications

TL;DR

This paper rigorously analyzes and extends the method of brackets, a heuristic technique for evaluating integrals in Feynman diagram calculations, by verifying its steps, proving its invariance, and introducing modifications through analytic continuation.

Contribution

It provides a formal verification of the method of brackets and proposes modifications based on analytic continuation to improve its applicability.

Findings

Verified the steps of the method of brackets

Proved independence from integrand representations

Introduced modifications using analytic continuation

Abstract

The method of brackets, consisting of a small number of heuristic rules, was created by Ivan Gonzalez for the evaluation of definite integrals appearing in the resolution of Feynman diagrams. The current work verifies each step of this method, proves the independence on different representations of the integrand, and also modifies the rule by further considering analytic continuation.