{"paper":{"title":"A New Noncommutative Product on the Fuzzy Two-Sphere Corresponding to the Unitary Representation of SU(2) and the Seiberg-Witten Map","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"K. Hayasaka, R. Nakayama, Y. Takaya","submitted_at":"2002-09-27T08:35:32Z","abstract_excerpt":"We obtain a new explicit expression for the noncommutative (star) product on the fuzzy two-sphere which yields a unitary representation. This is done by constructing a star product, $\\star_{\\lambda}$, for an arbitrary representation of SU(2) which depends on a continuous parameter $\\lambda$ and searching for the values of $\\lambda$ which give unitary representations. We will find two series of values: $\\lambda = \\lambda^{(A)}_j=1/(2j)$ and $\\lambda=\\lambda^{(B)}_j =-1/(2j+2)$, where j is the spin of the representation of SU(2). At $\\lambda = \\lambda^{(A)}_j$ the new star product $\\star_{\\lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0209240","kind":"arxiv","version":4},"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"}