{"paper":{"title":"Pointlike Hopf defects in Abelian projections","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Falk Bruckmann (FSU Jena)","submitted_at":"2000-12-01T13:24:14Z","abstract_excerpt":"We present a new kind of defect in Abelian Projections, stemming from pointlike zeros of second order. The corresponding topological quantity is the Hopf invariant pi_3(S^2) (rather than the winding number pi_2(S^2) for magnetic monopoles). We give a visualisation of this quantity and discuss the simplest non-trivial example, the Hopf map. Such defects occur in the Laplacian Abelian gauge in a non-trivial instanton sector. For general Abelian projections we show how an ensemble of Hopf defects accounts for the instanton number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0012004","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"}