{"id":"https://openalex.org/W3114324539","doi":"https://doi.org/10.22331/q-2021-06-04-468","title":"<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>a</mml:mi><mml:mo>\u00d7</mml:mo><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mi>c</mml:mi></mml:math> in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>D TQFT","display_name":"<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>a</mml:mi><mml:mo>\u00d7</mml:mo><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mi>c</mml:mi></mml:math> in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>D TQFT","publication_year":2021,"publication_date":"2021-06-04","ids":{"openalex":"https://openalex.org/W3114324539","doi":"https://doi.org/10.22331/q-2021-06-04-468","mag":"3114324539"},"language":"lv","primary_location":{"id":"doi:10.22331/q-2021-06-04-468","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-06-04-468","pdf_url":"https://quantum-journal.org/papers/q-2021-06-04-468/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-06-04-468/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076703255","display_name":"Matthew Buican","orcid":"https://orcid.org/0000-0001-8537-2759"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matthew Buican","raw_affiliation_strings":["CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100343209","display_name":"Linfeng Li","orcid":"https://orcid.org/0000-0003-0026-4850"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Linfeng Li","raw_affiliation_strings":["CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054308274","display_name":"Rajath Radhakrishnan","orcid":"https://orcid.org/0000-0003-1158-3320"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rajath Radhakrishnan","raw_affiliation_strings":["CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CRST and School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK","institution_ids":["https://openalex.org/I166337079"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I166337079"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.3521,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.90416662,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":null,"first_page":"468","last_page":"468"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/topological-quantum-field-theory","display_name":"Topological quantum field theory","score":0.6516322493553162},{"id":"https://openalex.org/keywords/anyon","display_name":"Anyon","score":0.5766383409500122},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5632414221763611},{"id":"https://openalex.org/keywords/topological-quantum-computer","display_name":"Topological quantum computer","score":0.5255005359649658},{"id":"https://openalex.org/keywords/gauge-theory","display_name":"Gauge theory","score":0.45347434282302856},{"id":"https://openalex.org/keywords/gauge-group","display_name":"Gauge group","score":0.43790072202682495},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.42827659845352173},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4277958869934082},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.42380034923553467},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4169902205467224},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40203121304512024},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3406229019165039},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.23438647389411926},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.20574888586997986},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13341939449310303}],"concepts":[{"id":"https://openalex.org/C7503960","wikidata":"https://www.wikidata.org/wiki/Q721094","display_name":"Topological quantum field theory","level":2,"score":0.6516322493553162},{"id":"https://openalex.org/C2777446375","wikidata":"https://www.wikidata.org/wiki/Q5528","display_name":"Anyon","level":4,"score":0.5766383409500122},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5632414221763611},{"id":"https://openalex.org/C187483380","wikidata":"https://www.wikidata.org/wiki/Q7825042","display_name":"Topological quantum computer","level":3,"score":0.5255005359649658},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.45347434282302856},{"id":"https://openalex.org/C2779430453","wikidata":"https://www.wikidata.org/wiki/Q15260871","display_name":"Gauge group","level":3,"score":0.43790072202682495},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.42827659845352173},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4277958869934082},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.42380034923553467},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4169902205467224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40203121304512024},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3406229019165039},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23438647389411926},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.20574888586997986},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13341939449310303}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2021-06-04-468","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-06-04-468","pdf_url":"https://quantum-journal.org/papers/q-2021-06-04-468/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.14689","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.14689","pdf_url":"https://arxiv.org/pdf/2012.14689","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:809a4b137b354b11bd9d9a26b944e7e2","is_oa":true,"landing_page_url":"https://doaj.org/article/809a4b137b354b11bd9d9a26b944e7e2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 468 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-06-04-468","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-06-04-468","pdf_url":"https://quantum-journal.org/papers/q-2021-06-04-468/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1615777802","display_name":"String Theory, Gauge Theory and Duality","funder_award_id":"ST/P000754/1","funder_id":"https://openalex.org/F4320334632","funder_display_name":"Science and Technology Facilities Council"},{"id":"https://openalex.org/G1757178473","display_name":null,"funder_award_id":"ST/P000754/1","funder_id":"https://openalex.org/F4320334632","funder_display_name":"Science and Technology Facilities Council"},{"id":"https://openalex.org/G2101047277","display_name":null,"funder_award_id":"URF\\R\\201011","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G3041411303","display_name":null,"funder_award_id":"RGF\\EA\\180093","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G6754200054","display_name":null,"funder_award_id":"ST/T000686/1","funder_id":"https://openalex.org/F4320334632","funder_display_name":"Science and Technology Facilities Council"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320334632","display_name":"Science and Technology Facilities Council","ror":"https://ror.org/057g20z61"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3114324539.pdf","grobid_xml":"https://content.openalex.org/works/W3114324539.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W1567388844","https://openalex.org/W1589940326","https://openalex.org/W1976366117","https://openalex.org/W1977656703","https://openalex.org/W1979574852","https://openalex.org/W2004608596","https://openalex.org/W2005028755","https://openalex.org/W2007185418","https://openalex.org/W2010316320","https://openalex.org/W2013679555","https://openalex.org/W2015242555","https://openalex.org/W2027197477","https://openalex.org/W2029635999","https://openalex.org/W2030249398","https://openalex.org/W2034225373","https://openalex.org/W2037653768","https://openalex.org/W2043115844","https://openalex.org/W2044534809","https://openalex.org/W2045293491","https://openalex.org/W2064709773","https://openalex.org/W2087123842","https://openalex.org/W2102571154","https://openalex.org/W2108641779","https://openalex.org/W2121834386","https://openalex.org/W2127058163","https://openalex.org/W2131970804","https://openalex.org/W2136497493","https://openalex.org/W2141708961","https://openalex.org/W2147015770","https://openalex.org/W2159478153","https://openalex.org/W2163085561","https://openalex.org/W2171784722","https://openalex.org/W2338043504","https://openalex.org/W2434896206","https://openalex.org/W2950457676","https://openalex.org/W2951623434","https://openalex.org/W2962741511","https://openalex.org/W2962921146","https://openalex.org/W2963083870","https://openalex.org/W2963312201","https://openalex.org/W2964299018","https://openalex.org/W2965988389","https://openalex.org/W2974009797","https://openalex.org/W2994880985","https://openalex.org/W3036060404","https://openalex.org/W3037553564","https://openalex.org/W3040224107","https://openalex.org/W3046175132","https://openalex.org/W3100010488","https://openalex.org/W3100355515","https://openalex.org/W3100433369","https://openalex.org/W3102482732","https://openalex.org/W3103872722","https://openalex.org/W3104442609","https://openalex.org/W3104964704","https://openalex.org/W3105828811","https://openalex.org/W3110035657","https://openalex.org/W3110973627","https://openalex.org/W3111704114","https://openalex.org/W3113185111","https://openalex.org/W3117224931","https://openalex.org/W3158585294","https://openalex.org/W3208368108","https://openalex.org/W4205236482","https://openalex.org/W4206688401","https://openalex.org/W4236539388"],"related_works":["https://openalex.org/W1989659413","https://openalex.org/W1580099613","https://openalex.org/W2040520938","https://openalex.org/W4313250721","https://openalex.org/W1976049856","https://openalex.org/W4378843399","https://openalex.org/W1975133581","https://openalex.org/W4296972660","https://openalex.org/W1638151122","https://openalex.org/W2004537505"],"abstract_inverted_index":{"We":[0,167],"study":[1,168],"the":[2,5,61,65,75,113,144,152,161,196],"implications":[3],"of":[4,14,48,60,64,92,115,130,136,146,160,163,174],"anyon":[6],"fusion":[7,165],"equation":[8],"<mml:math":[9,15,23,26,38,49,52,68,71,99,102,120,123,156],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>a</mml:mi><mml:mo>\u00d7</mml:mo><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mi>c</mml:mi></mml:math>":[10],"on":[11,151,188],"global":[12],"properties":[13],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>D":[16],"topological":[17],"quantum":[18],"field":[19],"theories":[20,149,183,186],"(TQFTs).":[21],"Here":[22],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>a</mml:mi></mml:math>":[24,50,69,100,121],"and":[25,51,70,98,101,122,179,192],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>b</mml:mi></mml:math>":[27,53,72,103,124],"are":[28,73],"anyons":[29],"that":[30,112],"fuse":[31],"together":[32],"to":[33,184],"give":[34],"a":[35,84,90,134,172],"unique":[36],"anyon,":[37],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>c</mml:mi></mml:math>.":[39],"As":[40],"is":[41,54,82],"well":[42],"known,":[43],"when":[44,83],"at":[45],"least":[46],"one":[47],"abelian,":[55],"such":[56,79,116],"equations":[57],"describe":[58],"aspects":[59],"one-form":[62],"symmetry":[63],"theory.":[66],"When":[67],"non-abelian,":[74],"most":[76],"obvious":[77],"way":[78],"fusions":[80,117],"arise":[81],"TQFT":[85,175],"can":[86,125],"be":[87,127],"resolved":[88],"into":[89],"product":[91],"TQFTs":[93],"with":[94],"trivial":[95],"mutual":[96],"braiding,":[97],"lie":[104],"in":[105,133,143,171],"separate":[106],"factors.":[107],"More":[108],"generally,":[109],"we":[110,138,198],"argue":[111],"appearance":[114],"for":[118],"non-abelian":[119],"also":[126],"an":[128],"indication":[129],"zero-form":[131],"symmetries":[132],"TQFT,":[135],"what":[137],"term":[139],"\"quasi-zero-form":[140],"symmetries\"":[141],"(as":[142],"case":[145],"discrete":[147,181],"gauge":[148,182,190],"based":[150,187],"largest":[153],"Mathieu":[154],"group,":[155],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>M</mml:mi><mml:mrow":[157],"class=\"MJX-TeXAtom-ORD\"><mml:mn>24</mml:mn></mml:mrow></mml:msub></mml:math>),":[158],"or":[159],"existence":[162],"non-modular":[164],"subcategories.":[166],"these":[169],"ideas":[170],"variety":[173],"settings":[176],"from":[177],"(twisted":[178],"untwisted)":[180],"Chern-Simons":[185],"continuous":[189],"groups":[191],"related":[193],"cosets.":[194],"Along":[195],"way,":[197],"prove":[199],"various":[200],"useful":[201],"theorems.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2021-01-05T00:00:00"}
