{"paper":{"title":"Dirac operator on the Riemann sphere","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. A. Abrikosov Jr","submitted_at":"2002-12-11T18:47:01Z","abstract_excerpt":"We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $\\lambda$ are nonzero integers. The eigenfunctions are two-component spinors that belong to representations of SU(2)-group with half-integer angular momenta $l = |\\lambda| - \\half$. They form on the sphere a complete orthonormal functional set alternative to conventional spherical spinors. The difference and relationship between the spherical spinors in question and the standard ones are explained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0212134","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/hep-th/0212134/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"}