{"paper":{"title":"Dirac-Coulomb operators with general charge distribution. II. The lowest eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"\\'Eric S\\'er\\'e, Maria J. Esteban, Mathieu Lewin","submitted_at":"2020-03-09T11:52:16Z","abstract_excerpt":"Consider the Coulomb potential $-\\mu\\ast|x|^{-1}$ generated by a non-negative finite measure $\\mu$. It is well known that the lowest eigenvalue of the corresponding Schr\\\"odinger operator $-\\Delta/2-\\mu\\ast|x|^{-1}$ is minimized, at fixed mass $\\mu(\\mathbb{R}^3)=\\nu$, when $\\mu$ is proportional to a delta. In this paper we investigate the conjecture that the same holds for the Dirac operator $-i\\alpha\\cdot\\nabla+\\beta-\\mu\\ast|x|^{-1}$. In a previous work on the subject we proved that this operator is self-adjoint when $\\mu$ has no atom of mass larger than or equal to 1, and that its eigenvalue"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.04051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.04051/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"}