{"paper":{"title":"An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Albert Mas, Luis Vega, Naiara Arrizabalaga","submitted_at":"2015-04-16T13:21:24Z","abstract_excerpt":"In this article we investigate spectral properties of the coupling $H+V_\\lambda$, where $H=-i\\alpha\\cdot\\nabla +m\\beta$ is the free Dirac operator in $\\mathbb R^3$, $m>0$ and $V_\\lambda$ is an electrostatic shell potential (which depends on a parameter $\\lambda\\in\\mathbb R$) located on the boundary of a smooth domain in $\\mathbb R^3$. Our main result is an isoperimetric-type inequality for the admissible range of $\\lambda$'s for which the coupling $H+V_\\lambda$ generates pure point spectrum in $(-m,m)$. That the ball is the unique optimizer of this inequality is also shown. Regarding some ingr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04220","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":""},"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"}