{"id":"https://openalex.org/W7214025769","doi":"https://doi.org/10.48550/arxiv.2609.23041","title":"The Requirement of (at least) Complex Structure for Quantum Mechanics","display_name":"The Requirement of (at least) Complex Structure for Quantum Mechanics","publication_year":2026,"publication_date":"2026-09-19","ids":{"openalex":"https://openalex.org/W7214025769","doi":"https://doi.org/10.48550/arxiv.2609.23041"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23041","pdf_url":"https://arxiv.org/pdf/2609.23041","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/2609.23041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134206980","display_name":"M. P. Vaughan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vaughan, M. P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5134206980"],"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.7720000147819519,"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"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.7720000147819519,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.21040000021457672,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.0017999999690800905,"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/complex-structure","display_name":"complex structure","score":0.7049999833106995},{"id":"https://openalex.org/keywords/hilbert-spaces","display_name":"Hilbert spaces","score":0.8320000171661377},{"id":"https://openalex.org/keywords/energy-conservation-physics","display_name":"energy conservation (physics)","score":0.9670000076293945},{"id":"https://openalex.org/keywords/time-evolution","display_name":"time evolution","score":0.9639999866485596},{"id":"https://openalex.org/keywords/quaternions","display_name":"quaternions","score":0.9089999794960022},{"id":"https://openalex.org/keywords/quantum-foundations","display_name":"quantum foundations","score":0.953000009059906}],"concepts":[{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.4634999930858612},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4521999955177307},{"id":"https://openalex.org/C186123792","wikidata":"https://www.wikidata.org/wiki/Q7390277","display_name":"SIC-POVM","level":5,"score":0.4512999951839447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4397999942302704},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4341999888420105},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4332999885082245},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42969998717308044},{"id":"https://openalex.org/C34829970","wikidata":"https://www.wikidata.org/wiki/Q845260","display_name":"Quantum statistical mechanics","level":3,"score":0.42910000681877136},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4205999970436096},{"id":"https://openalex.org/C138797146","wikidata":"https://www.wikidata.org/wiki/Q17105475","display_name":"Relational quantum mechanics","level":5,"score":0.3919000029563904},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.35850000381469727},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.3517000079154968},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3465999960899353},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.31769999861717224},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.3151000142097473},{"id":"https://openalex.org/C179153249","wikidata":"https://www.wikidata.org/wiki/Q5163228","display_name":"Consistent histories","level":5,"score":0.3142000138759613},{"id":"https://openalex.org/C194975256","wikidata":"https://www.wikidata.org/wiki/Q7269039","display_name":"Quantum dissipation","level":3,"score":0.3028999865055084},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C200717178","wikidata":"https://www.wikidata.org/wiki/Q606855","display_name":"Mathematical formulation of quantum mechanics","level":5,"score":0.28189998865127563},{"id":"https://openalex.org/C165973109","wikidata":"https://www.wikidata.org/wiki/Q894014","display_name":"Quantum probability","level":5,"score":0.2815999984741211},{"id":"https://openalex.org/C105295557","wikidata":"https://www.wikidata.org/wiki/Q5051814","display_name":"Categorical quantum mechanics","level":5,"score":0.2808000147342682},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23041","pdf_url":"https://arxiv.org/pdf/2609.23041","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.2609.23041","doi":"https://doi.org/10.48550/arxiv.2609.23041","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23041","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.23041","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23041","pdf_url":"https://arxiv.org/pdf/2609.23041","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/W7214025769.pdf","grobid_xml":"https://content.openalex.org/works/W7214025769.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1582339763","https://openalex.org/W4410348935","https://openalex.org/W7155087763"],"related_works":["https://openalex.org/W7134129021","https://openalex.org/W7167739430","https://openalex.org/W2947472376","https://openalex.org/W2891358157","https://openalex.org/W7134199073","https://openalex.org/W4417134196","https://openalex.org/W7072081466","https://openalex.org/W7131678204","https://openalex.org/W4412566097","https://openalex.org/W7134170075"],"abstract_inverted_index":{"It":[0,47,69],"is":[1,42,48,70,91,102],"argued":[2],"that":[3,15,73],"many":[4],"real-valued":[5],"constructions":[6,55],"of":[7,37,53,65,77,115,120],"quantum":[8,99,116],"mechanics":[9,117],"are":[10,20,61],"only":[11,103],"\\emph{nominally}":[12],"real":[13],"in":[14,44,98,118],"the":[16,28,75,88,113],"operators":[17],"and":[18,80],"states":[19],"restricted":[21],"to":[22,51,93],"impose":[23],"a":[24,63,104],"\\emph{complex":[25],"structure}":[26],"on":[27],"Hilbert":[29],"space.":[30],"That":[31],"is,":[32],"complex":[33,40,66,85],"algebra":[34],"between":[35],"pairs":[36],"elements":[38],"representing":[39],"numbers":[41],"preserved":[43],"these":[45,54],"formulations.":[46],"therefore":[49],"mistaken":[50],"think":[52],"as":[56,59,107,124],"being":[57],"`real'":[58],"they":[60],"actually":[62],"representation":[64],"linear":[67],"algebra.":[68],"then":[71],"shown":[72],"under":[74],"assumptions":[76],"state":[78],"normalisation":[79],"strict":[81],"energy":[82],"conservation,":[83],"this":[84],"structure":[86],"(at":[87],"very":[89],"least)":[90],"required":[92],"allow":[94],"for":[95],"time":[96],"evolution":[97],"mechanics.":[100],"This":[101],"\\emph{minimum}":[105],"requirement,":[106],"our":[108],"arguments":[109],"do":[110],"not":[111],"preclude":[112],"formulation":[114],"terms":[119],"hyper-complex":[121],"entities,":[122],"such":[123],"quaternions.":[125]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}
