{"paper":{"title":"A New $q$-Heisenberg Algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Julio Cesar Jaramillo Quiceno","submitted_at":"2025-05-31T20:16:42Z","abstract_excerpt":"This work introduces a novel $q$-$\\hbar$ deformation of the Heisenberg algebra, designed to unify and extend several existing $q$-deformed formulations. Starting from the canonical Heisenberg algebra defined by the commutation relation $[\\hat{x}, \\hat{p}] = i\\hbar$ on a Hilbert space \\cite{Zettili2009}, we survey a variety of $q$-deformed structures previously proposed by Wess \\cite{Wess2000}, Schm\\\"udgen \\cite{Schmudgen1999}, Wess--Schwenk \\cite{Wess-Schwenk1992}, Gaddis \\cite{Jasson-Gaddis2016}, and others. These frameworks involve position, momentum, and auxiliary operators that satisfy non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04248","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/2506.04248/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"}