{"id":"https://openalex.org/W3021720044","doi":"https://doi.org/10.22331/q-2020-11-30-367","title":"Quantum reference frames for general symmetry groups","display_name":"Quantum reference frames for general symmetry groups","publication_year":2020,"publication_date":"2020-11-30","ids":{"openalex":"https://openalex.org/W3021720044","doi":"https://doi.org/10.22331/q-2020-11-30-367","mag":"3021720044"},"language":"en","primary_location":{"id":"doi:10.22331/q-2020-11-30-367","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-11-30-367","pdf_url":"https://quantum-journal.org/papers/q-2020-11-30-367/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-2020-11-30-367/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Anne-Catherine de la Hamette","orcid":"https://orcid.org/0000-0003-4811-822X"},"institutions":[{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CA","CH"],"is_corresponding":true,"raw_author_name":"Anne-Catherine de la Hamette","raw_affiliation_strings":["Institute for Theoretical Physics, ETH Z\u00fcrich, Wolfgang-Pauli-Str. 27, 8093 Z\u00fcrich, Switzerland","Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada"],"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, ETH Z\u00fcrich, Wolfgang-Pauli-Str. 27, 8093 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada","institution_ids":["https://openalex.org/I183974707"]}]},{"author_position":"last","author":{"id":null,"display_name":"Thomas D. Galley","orcid":"https://orcid.org/0000-0002-8870-3215"},"institutions":[{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Thomas D. Galley","raw_affiliation_strings":["Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada"],"affiliations":[{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada","institution_ids":["https://openalex.org/I183974707"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I183974707","https://openalex.org/I35440088"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":8.4797,"has_fulltext":true,"cited_by_count":73,"citation_normalized_percentile":{"value":0.9858636,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"4","issue":null,"first_page":"367","last_page":"367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9294000267982483,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9294000267982483,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.011300000362098217,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.007699999958276749,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reference-frame","display_name":"Reference frame","score":0.8414000272750854},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.5676000118255615},{"id":"https://openalex.org/keywords/frame-of-reference","display_name":"Frame of reference","score":0.5618000030517578},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5291000008583069},{"id":"https://openalex.org/keywords/quantum-process","display_name":"Quantum process","score":0.4959000051021576},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.4871000051498413},{"id":"https://openalex.org/keywords/quantum-system","display_name":"Quantum system","score":0.4449000060558319},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.4372999966144562},{"id":"https://openalex.org/keywords/relational-quantum-mechanics","display_name":"Relational quantum mechanics","score":0.4122999906539917}],"concepts":[{"id":"https://openalex.org/C172849965","wikidata":"https://www.wikidata.org/wiki/Q3148875","display_name":"Reference frame","level":3,"score":0.8414000272750854},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.5676000118255615},{"id":"https://openalex.org/C74992021","wikidata":"https://www.wikidata.org/wiki/Q184876","display_name":"Frame of reference","level":2,"score":0.5618000030517578},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.4959000051021576},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4871000051498413},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4869999885559082},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.4449000060558319},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.4372999966144562},{"id":"https://openalex.org/C138797146","wikidata":"https://www.wikidata.org/wiki/Q17105475","display_name":"Relational quantum mechanics","level":5,"score":0.4122999906539917},{"id":"https://openalex.org/C105295557","wikidata":"https://www.wikidata.org/wiki/Q5051814","display_name":"Categorical quantum mechanics","level":5,"score":0.4043000042438507},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.3896999955177307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3765999972820282},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3668999969959259},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.351500004529953},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.349700003862381},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.3424000144004822},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3393000066280365},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.30379998683929443},{"id":"https://openalex.org/C5320026","wikidata":"https://www.wikidata.org/wiki/Q2122216","display_name":"Quantum information science","level":4,"score":0.28999999165534973},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C69975804","wikidata":"https://www.wikidata.org/wiki/Q1129622","display_name":"Self-reference","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.267300009727478},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2639000117778778},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25220000743865967}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2020-11-30-367","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-11-30-367","pdf_url":"https://quantum-journal.org/papers/q-2020-11-30-367/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:2004.14292","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.14292","pdf_url":"https://arxiv.org/pdf/2004.14292","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:f6348be74e05413b90ee1e1becebc24e","is_oa":true,"landing_page_url":"https://doaj.org/article/f6348be74e05413b90ee1e1becebc24e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 4, p 367 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2020-11-30-367","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-11-30-367","pdf_url":"https://quantum-journal.org/papers/q-2020-11-30-367/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":[],"funders":[{"id":"https://openalex.org/F4320312716","display_name":"Innovation, Science and Economic Development Canada","ror":"https://ror.org/03zp01h17"},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"},{"id":"https://openalex.org/F4320331473","display_name":"Ministry of Colleges and Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3021720044.pdf","grobid_xml":"https://content.openalex.org/works/W3021720044.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W578621958","https://openalex.org/W1485523613","https://openalex.org/W1968045764","https://openalex.org/W1969227315","https://openalex.org/W1977417311","https://openalex.org/W1993562105","https://openalex.org/W2004859216","https://openalex.org/W2009559386","https://openalex.org/W2021003280","https://openalex.org/W2024890519","https://openalex.org/W2026796483","https://openalex.org/W2051698581","https://openalex.org/W2053485921","https://openalex.org/W2055476267","https://openalex.org/W2061917421","https://openalex.org/W2076068770","https://openalex.org/W2084575582","https://openalex.org/W2135641715","https://openalex.org/W2138433381","https://openalex.org/W2140587459","https://openalex.org/W2148115906","https://openalex.org/W2206648280","https://openalex.org/W2285665705","https://openalex.org/W2468750585","https://openalex.org/W2597376000","https://openalex.org/W2608808167","https://openalex.org/W2619422756","https://openalex.org/W2778864117","https://openalex.org/W2797608247","https://openalex.org/W2890914617","https://openalex.org/W2896333123","https://openalex.org/W2898894554","https://openalex.org/W2921169191","https://openalex.org/W3032367681"],"related_works":[],"abstract_inverted_index":{"A":[0],"fully":[1],"relational":[2,32,132,224,246],"quantum":[3,12,16,20,54,125,150,186,214,247],"theory":[4],"necessarily":[5],"requires":[6],"an":[7,250],"account":[8],"of":[9,11,40,116,124,131,135,138,149,180,207,213,228,253],"changes":[10,179,212,227],"reference":[13,17,55,97,126,139,151,164,181,215,229,254],"frames,":[14],"where":[15,191],"frames":[18,56],"are":[19,27,112],"systems":[21,26,37,94,110,165,187],"relative":[22],"to":[23,58,71,92,101,235,243,258],"which":[24,34,84,111],"other":[25,117],"described.":[28],"By":[29],"introducing":[30],"a":[31,41,47,59,114,143,196,200],"formalism":[33,225],"identifies":[35],"coordinate":[36,90,109,118],"with":[38,154],"elements":[39],"symmetry":[42,193],"group<mml:math":[43,60,194],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>G</mml:mi></mml:math>,":[44],"we":[45,221],"define":[46,177],"general":[48],"operator":[49,66],"for":[50,67,183],"reversibly":[51,102],"changing":[52],"between":[53,104,108],"associated":[57],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>G</mml:mi></mml:math>.":[61,174],"This":[62],"generalises":[63],"the":[64,122,129,147,163,167,189,192,218,223,236],"known":[65],"translations":[68],"and":[69,74,99,134,160,169,185,210,226],"boosts":[70],"arbitrary":[72],"finite":[73],"locally":[75],"compact":[76],"groups,":[77],"including":[78],"non-Abelian":[79],"groups.":[80],"We":[81,120,141,175],"show":[82],"under":[83],"conditions":[85],"one":[86],"can":[87],"uniquely":[88],"assign":[89],"choices":[91],"physical":[93],"(to":[95],"form":[96],"frames)":[98],"how":[100],"transform":[103],"them,":[105],"providing":[106,204],"transformations":[107],"`in":[113],"superposition'":[115],"systems.":[119],"obtain":[121],"change":[123,137,148,252],"frame":[127,152,182,230,255],"from":[128],"principles":[130,156],"physics":[133],"coherent":[136],"frame.":[140],"prove":[142],"theorem":[144],"stating":[145],"that":[146],"consistent":[153],"these":[155],"is":[157],"unitary":[158],"if":[159,162],"only":[161],"carry":[166],"left":[168],"right":[170],"regular":[171],"representations":[172],"of<mml:math":[173],"also":[176],"irreversible":[178,211],"classical":[184],"in":[188,232,245],"case":[190],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>G</mml:mi></mml:math>is":[195],"semi-direct":[197],"product<mml:math":[198,202],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mo>\u22ca</mml:mo><mml:mi>P</mml:mi></mml:math>or":[199],"direct":[201],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mi>N</mml:mi><mml:mo>\u00d7</mml:mo><mml:mi>P</mml:mi></mml:math>,":[203],"multiple":[205],"examples":[206],"both":[208],"reversible":[209],"system":[216],"along":[217],"way.":[219],"Finally,":[220],"apply":[222],"developed":[231],"this":[233],"work":[234],"Wigner's":[237],"friend":[238],"scenario,":[239],"finding":[240],"similar":[241],"conclusions":[242],"those":[244],"mechanics":[248],"using":[249,261],"explicit":[251],"as":[256],"opposed":[257],"indirect":[259],"reasoning":[260],"measurement":[262],"operators.":[263]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":24},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2020-05-13T00:00:00"}