{"paper":{"title":"Constructive Quantum Field Theory on Curved Surfaces and Related Topics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.DG","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Jiasheng Lin","submitted_at":"2025-07-29T10:11:56Z","abstract_excerpt":"This is the Ph.D. thesis of the author. In this thesis, we construct the $ P(\\phi)_2 $ Quantum Field Theory (QFT) model on curved surfaces and show that it satisfies Segal's axioms (arXiv:2403.12804). An important ingredient in this construction is the use of a local regularization procedure to define the interaction as a random variable with respect to the Gaussian Free Field (GFF). We provide a counterexample demonstrating that spectral truncation regularization violates locality (arXiv:2312.15511). We then explain how Segal's formalism can be extended to the gluing of surfaces with slits, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.21655","kind":"arxiv","version":1},"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/2507.21655/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"}