{"paper":{"title":"Hardy-Lieb-Thirring Inequalities for Fractional Pauli Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Gonzalo A. Bley, S{\\o}ren Fournais","submitted_at":"2018-01-19T13:24:55Z","abstract_excerpt":"We provide lower bounds for the sum of the negative eigenvalues of the operator $|\\sigma\\cdot p_A|^{2s} - C_s/|x|^{2s} + V$ in three dimensions, where $s\\in (0, 1]$, covering the interesting physical cases $s = 1$ and $s = 1/2$. Here $\\sigma$ is the vector of Pauli matrices, $p_A = p - A$, with $p = -i\\nabla$ the three-dimensional momentum operator and $A$ a given magnetic vector potential, and $C_s$ is the critical Hardy constant, that is, the optimal constant in the Hardy inequality $|p|^{2s} \\geq C_s/|x|^{2s}$. If spin is neglected, results of this type are known in the literature as Hardy-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06398","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":""},"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"}