{"paper":{"title":"A criterion for the existence of non-real eigenvalues for a Dirac operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Diomba Sambou","submitted_at":"2015-08-10T21:35:55Z","abstract_excerpt":"The aim of this work is to explore the discrete spectrum generated by complex perturbations in $L^{2}(\\mathbb{R}^3,\\mathbb{C}^4)$ of the $3d$ Dirac operator $\\alpha \\cdot (-i\\nabla - \\textbf{A}) + m \\beta$ with variable magnetic field. Here, $\\alpha := (\\alpha_1,\\alpha_2,\\alpha_3)$ and $\\beta$ are $4 \\times 4$ Dirac matrices, and $m > 0$ is the mass of a particle. We give a simple criterion for the potentials to generate discrete spectrum near $\\pm m$. In the case of creation of non-real eigenvalues, this criterion gives also their location."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02434","kind":"arxiv","version":4},"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"}