{"paper":{"title":"Truncating Dyson-Schwinger Equations Based on Lefschetz Thimble Decomposition and Borel Resummation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Feiyu Peng, Hongfei Shu","submitted_at":"2024-10-17T09:15:46Z","abstract_excerpt":"We study the zero-dimensional prototype of the path integrals in quantum mechanics and quantum field theory, with the action $S(\\phi)=\\frac{\\sigma }{2}\\phi^{2}+\\frac{\\lambda}{4}\\phi^{4}$. Using the Lefschetz thimble decomposition and the saddle point expansion, we derive multiple asymptotic formal series of the correlation function associated with the perturbative and non-perturbative saddle points. Furthermore, we reconstruct the exact correlation function employing the Borel resummation. We then consider how to truncate the Dyson-Schwinger (DS) equations beginning with the perturbation expan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.13364","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.13364/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}