{"id":"https://openalex.org/W2123734726","doi":"https://doi.org/10.3390/sym3020134","title":"Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?","display_name":"Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?","publication_year":2011,"publication_date":"2011-03-31","ids":{"openalex":"https://openalex.org/W2123734726","doi":"https://doi.org/10.3390/sym3020134","mag":"2123734726"},"language":"en","primary_location":{"id":"doi:10.3390/sym3020134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym3020134","pdf_url":"https://www.mdpi.com/2073-8994/3/2/134/pdf?version=1301570066","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/3/2/134/pdf?version=1301570066","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Karim P. Y. Th\u00e9bault","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Karim P. Y. Th\u00e9bault","raw_affiliation_strings":["Centre for Time, School of Philosophical and Historical Enquiry, University of Sydney, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Time, School of Philosophical and Historical Enquiry, University of Sydney, Australia","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.6764,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70780033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"3","issue":"2","first_page":"134","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.7527999877929688,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.7527999877929688,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.08179999887943268,"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/T11683","display_name":"Quantum and Classical Electrodynamics","score":0.03689999878406525,"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/hilbert-space","display_name":"Hilbert space","score":0.7278000116348267},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6425999999046326},{"id":"https://openalex.org/keywords/canonical-quantization","display_name":"Canonical quantization","score":0.5813999772071838},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.5659999847412109},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4934000074863434},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.4325999915599823},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.3903999924659729},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.3619999885559082},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.3458000123500824}],"concepts":[{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7278000116348267},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6425999999046326},{"id":"https://openalex.org/C158913796","wikidata":"https://www.wikidata.org/wiki/Q5961083","display_name":"Canonical quantization","level":4,"score":0.5813999772071838},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5659999847412109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5076000094413757},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39629998803138733},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3743000030517578},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3619999885559082},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3391999900341034},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.33410000801086426},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3257000148296356},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C179578378","wikidata":"https://www.wikidata.org/wiki/Q2067074","display_name":"Canonical quantum gravity","level":5,"score":0.314300000667572},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3084999918937683},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.2939000129699707},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C161520196","wikidata":"https://www.wikidata.org/wiki/Q1366892","display_name":"Canonical transformation","level":3,"score":0.2703000009059906},{"id":"https://openalex.org/C41054515","wikidata":"https://www.wikidata.org/wiki/Q2000912","display_name":"Standard basis","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25200000405311584}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/sym3020134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym3020134","pdf_url":"https://www.mdpi.com/2073-8994/3/2/134/pdf?version=1301570066","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/ed3583c7-e718-4bd9-996d-0816742dd034","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/ed3583c7-e718-4bd9-996d-0816742dd034","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Th\u00e9bault, K P Y 2011, 'Quantisation, representation and reduction; How should we interpret the quantum Hamiltonian constraints of canonical gravity?', Symmetry, vol. 3, no. 2, pp. 134-154. https://doi.org/10.3390/sym3020134","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1108.4731","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1108.4731","pdf_url":"https://arxiv.org/pdf/1108.4731","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,"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:b31f248ad56842998c4deb49c85f4441","is_oa":true,"landing_page_url":"https://doaj.org/article/b31f248ad56842998c4deb49c85f4441","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":"Symmetry, Vol 3, Iss 2, Pp 134-154 (2011)","raw_type":"article"},{"id":"pmh:oai:epub.ub.uni-muenchen.de:17633","is_oa":true,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bvb:19-epub-17633-6","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.3390/sym3020134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym3020134","pdf_url":"https://www.mdpi.com/2073-8994/3/2/134/pdf?version=1301570066","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2123734726.pdf","grobid_xml":"https://content.openalex.org/works/W2123734726.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1570642002","https://openalex.org/W1947273351","https://openalex.org/W1971470664","https://openalex.org/W1976415611","https://openalex.org/W1978654044","https://openalex.org/W1997406347","https://openalex.org/W2017808716","https://openalex.org/W2020922227","https://openalex.org/W2027619753","https://openalex.org/W2033966297","https://openalex.org/W2061620121","https://openalex.org/W2066785380","https://openalex.org/W2069126550","https://openalex.org/W2073992954","https://openalex.org/W2095945737","https://openalex.org/W2098215080","https://openalex.org/W2126385467","https://openalex.org/W2170208120","https://openalex.org/W4231009334","https://openalex.org/W4233500204","https://openalex.org/W4298222025","https://openalex.org/W6632799846","https://openalex.org/W6659138324","https://openalex.org/W6789509932"],"related_works":[],"abstract_inverted_index":{"Hamiltonian":[0,92],"constraints":[1,12,56,93],"feature":[2],"in":[3,116],"the":[4,31,52,60,82,117,123],"canonical":[5,126],"formulation":[6],"of":[7,34,54,81,119,125],"general":[8,127],"relativity.":[9,128],"Unlike":[10],"typical":[11],"they":[13],"cannot":[14],"be":[15,112],"associated":[16],"with":[17,48],"a":[18,23,65,72],"reduction":[19,106],"procedure":[20],"leading":[21,70],"to":[22,57,64,71,76,122],"non-trivial":[24],"reduced":[25,84],"phase":[26],"space":[27,74],"and":[28,50,105,114],"this":[29],"means":[30],"physical":[32],"interpretation":[33],"their":[35],"quantum":[36,94],"analogues":[37],"is":[38],"ambiguous.":[39],"In":[40],"particular,":[41],"can":[42],"we":[43,90,101],"assume":[44],"that":[45,77,103],"\u201cquantisation":[46],"commutes":[47],"reduction\u201d":[49],"treat":[51],"promotion":[53],"these":[55],"operators":[58],"annihilating":[59],"wave":[61],"function,":[62],"according":[63],"Dirac":[66],"type":[67],"procedure,":[68],"as":[69],"Hilbert":[73],"equivalent":[75],"reached":[78],"by":[79],"quantisation":[80,104,124],"problematic":[83],"space?":[85],"If":[86],"not,":[87],"how":[88],"should":[89],"interpret":[91],"mechanically?":[95],"And":[96],"on":[97],"what":[98],"basis":[99],"do":[100],"assert":[102],"commute":[107],"anyway?":[108],"These":[109],"questions":[110],"will":[111],"refined":[113],"explored":[115],"context":[118],"modern":[120],"approaches":[121]},"counts_by_year":[{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}
