{"paper":{"title":"Spin, statistics, orientations, unitarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.AT","math.CT","math.MP"],"primary_cat":"math-ph","authors_text":"Theo Johnson-Freyd","submitted_at":"2015-07-22T19:49:23Z","abstract_excerpt":"A topological quantum field theory is Hermitian if it is both oriented and complex-valued, and orientation-reversal agrees with complex-conjugation. A field theory satisfies spin-statistics if it is both spin and super, and $360^\\circ$-rotation of the spin structure agrees with the operation of flipping the signs of all fermions. We set up a framework in which these two notions are precisely analogous. In this framework, field theories are defined over $\\mathrm{Vect}_{\\mathbb R}$, but rather than being defined in terms of a single tangential structure, they are defined in terms of a bundle of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06297","kind":"arxiv","version":6},"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"}