{"paper":{"title":"On Dirac operators with electrostatic \\delta-shell interactions of critical strength","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Jussi Behrndt, Markus Holzmann","submitted_at":"2016-12-07T15:28:50Z","abstract_excerpt":"In this paper we prove that the Dirac operator $A_\\eta$ with an electrostatic $\\delta$-shell interaction of critical strength $\\eta = \\pm 2$ supported on a $C^2$-smooth compact surface $\\Sigma$ is self-adjoint in $L^2(\\mathbb{R}^3;\\mathbb{C}^4)$, we describe the domain explicitly in terms of traces and jump conditions in $H^{-1/2}(\\Sigma; \\mathbb{C}^4)$, and we investigate the spectral properties of $A_\\eta$. While the non-critical interaction strengths $\\eta \\not= \\pm 2$ have received a lot of attention in the recent past, the critical case $\\eta = \\pm 2$ remained open. Our approach is based "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02290","kind":"arxiv","version":3},"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"}