{"id":"https://openalex.org/W7207630833","doi":"https://doi.org/10.48550/arxiv.2609.01894","title":"A Hilbert Module Approach to Classical and Quantum Reference Frames","display_name":"A Hilbert Module Approach to Classical and Quantum Reference Frames","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7207630833","doi":"https://doi.org/10.48550/arxiv.2609.01894"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01894","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01894","pdf_url":"https://arxiv.org/pdf/2609.01894","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01894","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135883112","display_name":"Lucus Brady","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Brady, Lucus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5135883112"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9901999831199646,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9901999831199646,"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"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.003000000026077032,"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"}},{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/reference-frames","display_name":"reference frames","score":0.8080000281333923},{"id":"https://openalex.org/keywords/quantum-reference-frames","display_name":"quantum reference frames","score":0.8740000128746033},{"id":"https://openalex.org/keywords/hilbert-modules","display_name":"Hilbert modules","score":0.9869999885559082},{"id":"https://openalex.org/keywords/c-algebras","display_name":"C*-algebras","score":0.9409999847412109},{"id":"https://openalex.org/keywords/c-dynamical-systems","display_name":"C*-dynamical systems","score":0.9819999933242798},{"id":"https://openalex.org/keywords/quantum-foundations","display_name":"quantum foundations","score":0.3440000116825104}],"concepts":[{"id":"https://openalex.org/C186123792","wikidata":"https://www.wikidata.org/wiki/Q7390277","display_name":"SIC-POVM","level":5,"score":0.5999000072479248},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5467000007629395},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5329999923706055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.527899980545044},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.5004000067710876},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.49570000171661377},{"id":"https://openalex.org/C172849965","wikidata":"https://www.wikidata.org/wiki/Q3148875","display_name":"Reference frame","level":3,"score":0.4593999981880188},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4433000087738037},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.42260000109672546},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4156000018119812},{"id":"https://openalex.org/C179957908","wikidata":"https://www.wikidata.org/wiki/Q907206","display_name":"POVM","level":5,"score":0.39719998836517334},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.39640000462532043},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.36079999804496765},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.36070001125335693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34769999980926514},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C105295557","wikidata":"https://www.wikidata.org/wiki/Q5051814","display_name":"Categorical quantum mechanics","level":5,"score":0.2903999984264374},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2897000014781952},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.2831999957561493},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C91717678","wikidata":"https://www.wikidata.org/wiki/Q1135332","display_name":"Quantum teleportation","level":5,"score":0.2754000127315521},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C8492334","wikidata":"https://www.wikidata.org/wiki/Q7269100","display_name":"Quantum spacetime","level":4,"score":0.26989999413490295},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2572000026702881},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01894","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01894","pdf_url":"https://arxiv.org/pdf/2609.01894","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.01894","doi":"https://doi.org/10.48550/arxiv.2609.01894","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01894","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.01894","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01894","pdf_url":"https://arxiv.org/pdf/2609.01894","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207630833.pdf","grobid_xml":"https://content.openalex.org/works/W7207630833.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4414580881"],"related_works":["https://openalex.org/W2166361939","https://openalex.org/W3159551655","https://openalex.org/W1568450341","https://openalex.org/W3017456225","https://openalex.org/W3098833554","https://openalex.org/W2256548765","https://openalex.org/W7099363185","https://openalex.org/W968876197","https://openalex.org/W4249690967","https://openalex.org/W3156637810"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,39],"present":[4],"a":[5,31],"model":[6,29,44],"for":[7,13,34,61],"classical":[8,28,63],"and":[9,19,38,64],"quantum":[10,36,43,52,65],"reference":[11,53,66],"frames":[12],"$C^*$-algebras":[14],"by":[15],"utilizing":[16],"Hilbert":[17,47],"modules":[18],"equivariant":[20],"correspondences":[21],"of":[22,51],"$C^*$-dynamical":[23],"systems.":[24],"We":[25,55],"show":[26],"the":[27,35,42,46],"provides":[30],"commutative":[32],"baseline":[33],"model,":[37],"discuss":[40],"how":[41],"encodes":[45],"space":[48],"operational":[49],"formulation":[50],"frames.":[54,67],"also":[56],"include":[57],"various":[58],"explicit":[59],"examples":[60],"both":[62]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}