{"paper":{"title":"Expressions of algebra elements and transcendental noncommutative calculus","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Akira Yoshioka, Hideki Omori, Naoya Miyazaki, Yoshiaki Maeda","submitted_at":"2007-11-16T13:07:21Z","abstract_excerpt":"Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that $\\frac{1}{i\\h}uv$ in the Weyl algebra is naturally viewed as an indeterminate living in a discrete set $\\mathbb{N}{+}{1/2}$ {\\it or} ${-}(\\mathbb{N}{+}{1/2})$ . This may yield a more mathematical understanding of Dirac's positron theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.2608","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}