{"paper":{"title":"Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Carolyn Gordon, David Webb, Dorothee Schueth, William D. Kirwin","submitted_at":"2010-09-02T12:16:55Z","abstract_excerpt":"We construct pairs of compact K\\\"ahler-Einstein manifolds $(M_i,g_i,\\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\\bigwedge^n T^*M_i$ has Chern class $[\\omega_i/2\\pi]$, and for each integer $k$ the tensor powers $L_1^{\\otimes k}$ and $L_2^{\\otimes k}$ are isospectral for the bundle Laplacian associated with the canonical connection, while $M_1$ and $M_2$ -- and hence $T^*M_1$ and $T^*M_2$ -- are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0404","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"}