Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series

Alessio Maiezza () and Juan Carlos Vasquez
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Alessio Maiezza: Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell’Aquila, via Vetoio, 67100 L’Aquila, Italy
Juan Carlos Vasquez: Department of Physics and Astronomy, Amherst College, Amherst, MA 01002, USA

Mathematics, 2024, vol. 12, issue 19, 1-18

Abstract: We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent formulation of renormalized perturbation theory in quantum field theory. We use the Borel–Padé approximant and classical analysis to determine the analytic structure of the solution using the first few terms of its asymptotic series. Afterward, we build an approximant, consistent with the resurgent properties of the equation. The procedure gives an approximate expression for the Borel–Ecalle resummation of the solution useful for practical applications. Connections with other physical applications are also discussed.

Keywords: asymptotic series; quantum field theory; resummation; renormalons; ordinary differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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