{"id":"https://openalex.org/W185191707","doi":null,"title":"Quantum Hall Effect and Hierarchy of Planck Constants","display_name":"Quantum Hall Effect and Hierarchy of Planck Constants","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W185191707","mag":"185191707"},"language":"en","primary_location":{"id":"mag:185191707","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/0812.0006v3.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079866489","display_name":"Matti Pitk\u00e4nen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Matti Pitk\u00e4nen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5079866489"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.5023999810218811,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.5023999810218811,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.17520000040531158,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.07519999891519547,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-hall-effect","display_name":"quantum Hall effect","score":0.9200000166893005},{"id":"https://openalex.org/keywords/fractional-quantum-hall-effect","display_name":"fractional quantum Hall effect","score":0.8569999933242798},{"id":"https://openalex.org/keywords/anyons","display_name":"anyons","score":0.9800000190734863},{"id":"https://openalex.org/keywords/causal-diamond","display_name":"causal diamond","score":0.6880000233650208},{"id":"https://openalex.org/keywords/big-book","display_name":"big book","score":0.5609999895095825},{"id":"https://openalex.org/keywords/kahler-structures","display_name":"K\u00e4hler structures","score":0.7409999966621399},{"id":"https://openalex.org/keywords/fractional-filling-factor","display_name":"fractional filling factor","score":0.7310000061988831},{"id":"https://openalex.org/keywords/tgd","display_name":"TGD","score":0.628000020980835}],"concepts":[{"id":"https://openalex.org/C166126730","wikidata":"https://www.wikidata.org/wiki/Q725309","display_name":"Planck","level":2,"score":0.727807879447937},{"id":"https://openalex.org/C187483380","wikidata":"https://www.wikidata.org/wiki/Q7825042","display_name":"Topological quantum computer","level":3,"score":0.5949957966804504},{"id":"https://openalex.org/C66870719","wikidata":"https://www.wikidata.org/wiki/Q1030113","display_name":"Fractional quantum Hall effect","level":5,"score":0.5613740086555481},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5547517538070679},{"id":"https://openalex.org/C30539742","wikidata":"https://www.wikidata.org/wiki/Q5997","display_name":"Fine-structure constant","level":3,"score":0.5428228378295898},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.5025608539581299},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4870153069496155},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.47399675846099854},{"id":"https://openalex.org/C197111296","wikidata":"https://www.wikidata.org/wiki/Q122894","display_name":"Planck constant","level":3,"score":0.46292945742607117},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42846062779426575},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4273050129413605},{"id":"https://openalex.org/C118697519","wikidata":"https://www.wikidata.org/wiki/Q207387","display_name":"Planck length","level":5,"score":0.4264928102493286},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.40632909536361694},{"id":"https://openalex.org/C200369452","wikidata":"https://www.wikidata.org/wiki/Q1047822","display_name":"Quantum Hall effect","level":3,"score":0.40097108483314514},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40018197894096375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37543028593063354},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33230912685394287},{"id":"https://openalex.org/C192638945","wikidata":"https://www.wikidata.org/wiki/Q468999","display_name":"Planck scale","level":4,"score":0.2655943036079407},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.1505623757839203},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11639413237571716},{"id":"https://openalex.org/C145727058","wikidata":"https://www.wikidata.org/wiki/Q7269101","display_name":"Quantum spin Hall effect","level":4,"score":0.1041536033153534},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.10401245951652527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08433890342712402},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:185191707","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/0812.0006v3.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1558058382","https://openalex.org/W1668162707","https://openalex.org/W1927245941","https://openalex.org/W1983232932","https://openalex.org/W2007185418","https://openalex.org/W2033091009","https://openalex.org/W2036840403","https://openalex.org/W2140678588","https://openalex.org/W2159566537","https://openalex.org/W2164171842","https://openalex.org/W2170043777","https://openalex.org/W2170767514","https://openalex.org/W2507911449","https://openalex.org/W2612451553"],"related_works":["https://openalex.org/W2029683030","https://openalex.org/W7155384096","https://openalex.org/W2950879931","https://openalex.org/W1987617226","https://openalex.org/W3186900330","https://openalex.org/W1975493223","https://openalex.org/W1974861603","https://openalex.org/W7220590898","https://openalex.org/W6922614817","https://openalex.org/W2804607649"],"abstract_inverted_index":{"I":[0,150],"have":[1],"already":[2],"earlier":[3],"proposed":[4],"the":[5,27,67,91,116,123,172,176,181],"explanation":[6],"of":[7,12,17,19,26,58,66,77,84,93,118,125,175],"FQHE,":[8],"anyons,":[9],"and":[10,48,60,74,87,99,101,170],"fractionization":[11],"quantum":[13],"numbers":[14],"in":[15,103],"terms":[16],"hierarchy":[18],"Planck":[20,94,110,127],"constants":[21,95],"realized":[22],"as":[23,56],"a":[24,36,144,161],"generalization":[25],"imbedding":[28,178],"space":[29,179],"H":[30],"=":[31],"M4":[32,119],"x":[33],"CP2":[34,47,100],"to":[35,46,49,71,97,122,152],"book":[37,41],"like":[38,42],"structure.":[39],"The":[40,64,108,129,158],"structure":[43,174],"applies":[44],"separately":[45],"causal":[50],"diamonds":[51],"(CD":[52],"\u2282":[53],"M4)":[54],"defined":[55],"intersections":[57],"future":[59],"past":[61],"directed":[62],"light-cones.":[63],"pages":[65],"Big":[68],"Book":[69],"correspond":[70],"singular":[72],"coverings":[73],"factor":[75,136],"spaces":[76],"CD":[78,85,98],"(CP2)":[79,86],"glued":[80],"along":[81],"2-D":[82],"subspace":[83],"are":[88],"labeled":[89],"by":[90,143],"values":[92],"assignable":[96],"appearing":[102],"Lie":[104],"algebra":[105],"commutation":[106],"relations.":[107],"observed":[109],"constant":[111],"h,":[112],"whose":[113],"square":[114],"defines":[115],"scale":[117],"metric":[120],"corresponds":[121],"ratio":[124],"these":[126],"constants.":[128],"key":[130],"observation":[131],"is":[132,140,160],"that":[133],"fractional":[134],"filling":[135],"results":[137],"if":[138],"h":[139],"scaled":[141],"up":[142],"rational":[145],"number.":[146],"In":[147],"this":[148,156],"chapter":[149],"try":[151],"formulate":[153],"more":[154],"precisely":[155],"idea.":[157],"outcome":[159],"rather":[162],"detailed":[163],"view":[164],"about":[165,171],"anyons":[166],"on":[167,180],"one":[168],"hand,":[169],"Kahler":[173],"generalized":[177],"other":[182],"hand.":[183]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2016-06-24T00:00:00"}
