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

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.