{"paper":{"title":"On the approximation of the Dirac operator coupled with confining Lorentz scalar $\\delta$-shell interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Mahdi Zreik","submitted_at":"2024-04-11T14:25:00Z","abstract_excerpt":"Let $\\Omega_+\\subset\\mathbb{R}^{3}$ be a fixed bounded domain with boundary $\\Sigma = \\partial\\Omega_{+}$. We consider $\\mathcal{U}^\\varepsilon$ a tubular neighborhood of the surface $\\Sigma$ with a thickness parameter $\\varepsilon>0$, and we define the perturbed Dirac operator $\\mathfrak{D}^{\\varepsilon}_{M}=D_m +M\\beta \\mathbb{1}_{\\mathcal{U}^{\\varepsilon}},$ with $D_m$ the free Dirac operator, $M>0$, and $\\mathbb{1}_{\\mathcal{U }^{\\varepsilon}}$ the characteristic function of $\\mathcal{U}^{\\varepsilon}$. Then, in the norm resolvent sense, the Dirac operator $\\mathfrak{D}^{\\varepsilon}_M$ co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07784","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/2404.07784/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"}