{"paper":{"title":"On Jean-Marie Souriau's geometric quantization of the relativistic electron","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"G\\'ery de Saxc\\'e","submitted_at":"2026-05-31T09:39:12Z","abstract_excerpt":"The aim of this paper is to revisit, in Souriau's book \"Structure of Dynamical Systems\", the chapter devoted to the geometric quantization where the justifications of important results and formulae are not given and are difficult to prove. After recalling the coadjoint orbit method and its application to the relativistic particle with spin, we state and prove two keystone theorems that allow to equip its prequantum manifold with the symplectic and contact structures. We apply them to the relativistic particle with spin 1/2, leading to the Dirac equation and the conservation of the probability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01121","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/2606.01121/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"}