{"paper":{"title":"Mean-Field Bose--Einstein Condensation and Condensate Ideals in the Resolvent Algebra","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Yoshitsugu Sekine","submitted_at":"2026-07-02T14:51:05Z","abstract_excerpt":"This paper studies the imperfect Bose gas after the Kac density law and the mean-field Euler equations have selected a condensed density with positive zero-mode excess. In this BEC regime the selected chemical potential cancels the mean-field shift, so the selected one-particle Hamiltonian is exactly the free one. The resulting zero-mode covariance defines a mean-field BEC ideal in the resolvent algebra, while the nonregular quotient and the direct-integral center record distinct representation-theoretic data. Occupation-number and Brownian-loop formulations recover the same density selection,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02264","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/2607.02264/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"}