{"corpus_id":13016949,"paper_sha":"7ea0ed26f96c364bd11e04bcfedf4d4c21d8f630","doi":"10.1007/BF02101806","arxiv_id":"funct-an/9406005","pmid":null,"pmcid":null,"mag_id":2169298284,"dblp_id":null,"acl_id":null,"title":"An algebraic spin and statistics theorem","year":1994,"publication_date":"1994-06-23","venue":"","journal":{"name":"Communications in Mathematical Physics","pages":"517-533","volume":"172"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Physics"],"reference_count":56,"citation_count":124,"influential_citation_count":16,"is_open_access":false,"arxiv_categories":["funct-an","hep-th","math.OA"],"arxiv_license":null,"arxiv_journal_ref":"Commun.Math.Phys.172:517,1995; Commun.Math.Phys.172:517-534,1995","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional spacetime. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.","claims":[{"public_id":"cl_88efee8d1910dac24216a32c294d0daa","status":"active","text":"A spin-statistics theorem and a PCT theorem are obtained in the context of superselection sectors in Quantum Field Theory on a 4-dimensional spacetime.","confidence":0.93,"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_88efee8d1910dac24216a32c294d0daa"},{"public_id":"cl_7e9daf27b5b5953d3f13d7d8fa72f98b","status":"active","text":"Local algebras generated by Wightman fields satisfy the geometric modular action property by virtue of the Bisognano-Wichmann theorem, motivating its use as a natural primitive assumption.","confidence":0.9,"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_7e9daf27b5b5953d3f13d7d8fa72f98b"},{"public_id":"cl_34406056b45b758a3970a70100bffea0","status":"active","text":"The primitive assumption adopted is that modular groups of von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations.","confidence":0.92,"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/claims/cl_34406056b45b758a3970a70100bffea0"}],"concepts":[{"public_id":"co_21fd5624a51a96f650bcb2527240188c","status":"active","name":"PCT theorem","description":"A theorem asserting the combined symmetry of parity, charge conjugation, and time reversal in quantum field theory, derived here in the algebraic setting.","types":["theorem"],"aliases":["CPT theorem"],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_21fd5624a51a96f650bcb2527240188c"},{"public_id":"co_3921b1337ba8e0abe999bdd1af627542","status":"active","name":"von Neumann algebras of local observables","description":"Operator algebras associated with bounded spacetime regions whose modular structure encodes geometric symmetry properties in this paper.","types":["mathematical structure"],"aliases":[],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_3921b1337ba8e0abe999bdd1af627542"},{"public_id":"co_512a8aeb18888bfdf03eb1a11bfcd998","status":"active","name":"modular groups","description":"One-parameter automorphism groups associated with von Neumann algebras and cyclic separating vectors via the Tomita-Takesaki modular theory, assumed here to act as Lorentz boosts.","types":["mathematical structure"],"aliases":["modular automorphism groups"],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_512a8aeb18888bfdf03eb1a11bfcd998"},{"public_id":"co_56f5eacce950a0ffaa51718b048131b0","status":"active","name":"Wightman fields","description":"Quantum fields satisfying the Wightman axioms whose local algebras are known by the Bisognano-Wichmann theorem to have the required geometric modular action.","types":["concept","mathematical object"],"aliases":[],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_56f5eacce950a0ffaa51718b048131b0"},{"public_id":"co_6bbf76d4a69e46d7415b9c1f111c110f","status":"active","name":"Lorentz transformations","description":"Linear symmetry transformations of Minkowski spacetime preserving the metric, identified here as the geometric action of modular groups on wedge region algebras.","types":["symmetry transformation"],"aliases":["pure Lorentz transformations"],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_6bbf76d4a69e46d7415b9c1f111c110f"},{"public_id":"co_6f2cf686c70a420d0bd8e6bad4fe4c76","status":"active","name":"Bisognano-Wichmann theorem","description":"A theorem establishing that the modular group of the local algebra for a wedge region generated by Wightman fields acts geometrically as Lorentz boosts.","types":["theorem"],"aliases":[],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_6f2cf686c70a420d0bd8e6bad4fe4c76"},{"public_id":"co_daff7adbb973d6cc58b1ea46d1897ef3","status":"active","name":"superselection sectors","description":"Distinct irreducible subspaces of the Hilbert space in algebraic quantum field theory that cannot be superposed by local operations, providing the framework for this analysis.","types":["theoretical framework","concept"],"aliases":[],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_daff7adbb973d6cc58b1ea46d1897ef3"},{"public_id":"co_e2a0a627597993d4652414ba864994ec","status":"active","name":"Quantum Field Theory","description":"The physical framework combining quantum mechanics and special relativity, studied here on 4-dimensional spacetime using algebraic methods.","types":["theoretical framework"],"aliases":["QFT"],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_e2a0a627597993d4652414ba864994ec"},{"public_id":"co_e632b3bfeda6b4de0d1ec9d976d4a99c","status":"active","name":"wedge regions","description":"Causally complete spacetime regions (wedge-shaped in Minkowski space) whose associated algebras have modular groups acting as pure Lorentz transformations.","types":["spacetime region"],"aliases":[],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_e632b3bfeda6b4de0d1ec9d976d4a99c"},{"public_id":"co_fb1b254da5c05a9312673241ee5c3a89","status":"active","name":"spin-statistics theorem","description":"A theorem relating the intrinsic spin of particles to their statistical behavior (bosonic or fermionic), derived here algebraically within the superselection sector framework.","types":["theorem"],"aliases":[],"contributors":[{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["extraction"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"url":"https://sah.borca.ai/concepts/co_fb1b254da5c05a9312673241ee5c3a89"}],"external_ids":{"DOI":"10.1007/BF02101806","ArXiv":"funct-an/9406005","PubMed":null,"PubMedCentral":null,"MAG":2169298284,"DBLP":null,"ACL":null},"open_access":{"is_open_access":true,"pdf_url":"https://arxiv.org/pdf/funct-an/9406005","landing_url":"https://arxiv.org/abs/funct-an/9406005","source":"arxiv","pdf_url_source":"derived_arxiv","license":null,"reason":null},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":true,"full_text_source":"arxiv","count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":630773,"paper_uid":"3cc49c7b-efde-48ce-9fc9-cac1e46ef654","canonical_identity":{"paper_id":630773,"paper_uid":"3cc49c7b-efde-48ce-9fc9-cac1e46ef654","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/13016949"}