Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912054986670080 |
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| author | Maiezza, Alessio Vasquez, Juan Carlos |
| author_facet | Maiezza, Alessio Vasquez, Juan Carlos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series Maiezza, Alessio Vasquez, Juan Carlos Mathematical Physics High Energy Physics - Theory 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. |
| title | Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.20458 |