{"paper":{"title":"Symmetry Regularization of 1D Generalized Coulomb Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Guowu Meng, Junwei Ma, Zhanqiang Bai","submitted_at":"2026-06-08T00:56:29Z","abstract_excerpt":"For the 1D generalized Coulomb problems--a family that includes the quantizations of the 1D generalized Kepler problems of Ma-Meng-Xiao \\cite{MMX2025}--we construct two explicit unitary intertwiners $\\hat\\iota_{\\pm}$, the quantum analogs of the classical symmetry regularization maps $\\iota_{\\pm}$ of \\cite{MMX2025}, that unitarily identify each $H_{\\kappa}$-energy-definite portion of the Hilbert space $L^{2}(\\mathbb{R}_{>0},\\mathrm{d}q)$ with a unitary lowest-weight representation of $\\widetilde{\\mathrm{SL}}(2,\\mathbb{R})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08900","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/2606.08900/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"}