{"id":"https://openalex.org/W7211898059","doi":"https://doi.org/10.48550/arxiv.2609.05237","title":"Representation Theory of Canonical Commutation Relations Arising from the Quantization of the Klein-Gordon Equation with an External Potential","display_name":"Representation Theory of Canonical Commutation Relations Arising from the Quantization of the Klein-Gordon Equation with an External Potential","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7211898059","doi":"https://doi.org/10.48550/arxiv.2609.05237"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.05237","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05237","pdf_url":"https://arxiv.org/pdf/2609.05237","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/2609.05237","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037400929","display_name":"Yasumichi Matsuzawa","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Matsuzawa, Yasumichi","raw_affiliation_strings":["Department of Mathematics , Faculty of Education , Shinshu University , 6-Ro , Nishi-nagano , Nagano 380-8544 , Japan,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Faculty of Education , Shinshu University , 6-Ro , Nishi-nagano , Nagano 380-8544 , Japan,","institution_ids":["https://openalex.org/I137975476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148807050","display_name":"Itaru Sasaki","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Sasaki, Itaru","raw_affiliation_strings":["Department of Mathematics , Faculty of Science , Shinshu University , Matsumoto 390-8621 , Japan,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Faculty of Science , Shinshu University , Matsumoto 390-8621 , Japan,","institution_ids":["https://openalex.org/I137975476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040046878","display_name":"Akito Suzuki","orcid":"https://orcid.org/0000-0002-4140-5990","observed_orcids":["https://orcid.org/0000-0002-4140-5990"]},"institutions":[{"id":"https://openalex.org/I3132389022","display_name":"Komatsu University","ror":"https://ror.org/010b0td06","country_code":"JP","type":"education","lineage":["https://openalex.org/I3132389022"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Suzuki, Akito","raw_affiliation_strings":["Department of Production Systems Engineering and Sciences , Komatsu University , Awazu Cam- pus , Nu 1-3 Shicho-machi , Komatsu , Ishikawa 923-8511 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Production Systems Engineering and Sciences , Komatsu University , Awazu Cam- pus , Nu 1-3 Shicho-machi , Komatsu , Ishikawa 923-8511 , Japan","institution_ids":["https://openalex.org/I3132389022"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9394999742507935,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9394999742507935,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.050999999046325684,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0015999999595806003,"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/canonical-commutation-relations","display_name":"canonical commutation relations","score":0.9089999794960022},{"id":"https://openalex.org/keywords/weyl-representation","display_name":"Weyl representation","score":0.9919999837875366},{"id":"https://openalex.org/keywords/equivalence-of-representations","display_name":"representation equivalence","score":0.6439999938011169},{"id":"https://openalex.org/keywords/klein-gordon-equation","display_name":"Klein-Gordon equation","score":0.8939999938011169},{"id":"https://openalex.org/keywords/external-potential","display_name":"external potential","score":0.9860000014305115},{"id":"https://openalex.org/keywords/schrodinger-operators","display_name":"Schr\u00f6dinger operators","score":0.9950000047683716},{"id":"https://openalex.org/keywords/mass-dependence","display_name":"mass dependence","score":0.503000020980835},{"id":"https://openalex.org/keywords/short-range-potentials","display_name":"short-range potentials","score":0.796999990940094},{"id":"https://openalex.org/keywords/quantum-field-theory","display_name":"quantum field theory","score":0.5170000195503235}],"concepts":[{"id":"https://openalex.org/C2780147050","wikidata":"https://www.wikidata.org/wiki/Q5155085","display_name":"Commutation","level":3,"score":0.6362000107765198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.607200026512146},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5503000020980835},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.5285000205039978},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4896000027656555},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4408000111579895},{"id":"https://openalex.org/C158913796","wikidata":"https://www.wikidata.org/wiki/Q5961083","display_name":"Canonical quantization","level":4,"score":0.413100004196167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4007999897003174},{"id":"https://openalex.org/C31836371","wikidata":"https://www.wikidata.org/wiki/Q1856609","display_name":"Scalar potential","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C94618114","wikidata":"https://www.wikidata.org/wiki/Q7301169","display_name":"Real representation","level":3,"score":0.3434000015258789},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.32820001244544983},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.32170000672340393},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.311599999666214},{"id":"https://openalex.org/C207060392","wikidata":"https://www.wikidata.org/wiki/Q1353947","display_name":"Second quantization","level":4,"score":0.3010999858379364},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2750000059604645},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27379998564720154},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C187268509","wikidata":"https://www.wikidata.org/wiki/Q1402884","display_name":"Field theory (psychology)","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C2776122010","wikidata":"https://www.wikidata.org/wiki/Q10359539","display_name":"Unitary representation","level":3,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.05237","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05237","pdf_url":"https://arxiv.org/pdf/2609.05237","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.2609.05237","doi":"https://doi.org/10.48550/arxiv.2609.05237","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.05237","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:2609.05237","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05237","pdf_url":"https://arxiv.org/pdf/2609.05237","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":[{"id":"https://openalex.org/G3769011869","display_name":"Spectral analysis of quantum fields using Bogoliubov transformation","funder_award_id":"20K03628","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4938283963","display_name":"Limit theorem for quantum walks interacting with environment","funder_award_id":"23K03229","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5654385062","display_name":"A comprehensive study on the mathematical aspects of metallic ferromagnetism","funder_award_id":"23K25783","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7903781755","display_name":"\u91cf\u5b50\u30a6\u30a9\u30fc\u30af\u306b\u304a\u3051\u308b\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u76f8\u306e\u6570\u5b66\u7684\u7814\u7a76","funder_award_id":"24K06755","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211898059.pdf","grobid_xml":"https://content.openalex.org/works/W7211898059.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7208787889"],"related_works":["https://openalex.org/W2342803416","https://openalex.org/W2911300577","https://openalex.org/W7096420715","https://openalex.org/W2006560696","https://openalex.org/W3138684357","https://openalex.org/W7036638928","https://openalex.org/W7014956129","https://openalex.org/W2069499356","https://openalex.org/W2607033596","https://openalex.org/W2214887170"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,6,20,33,43,47,58,67,73,78,81,83,91,96,99,104,110],"Weyl":[3,34,68],"representation":[4,35],"of":[5,22,60,95],"canonical":[7],"commutation":[8],"relations":[9],"for":[10],"a":[11,14],"model":[12],"describing":[13],"quantized":[15],"massive":[16],"scalar":[17],"field":[18],"under":[19],"influence":[21],"an":[23],"external":[24],"potential.":[25],"The":[26],"main":[27],"problem":[28,54],"is":[29,55],"to":[30,38,42,57],"determine":[31],"whether":[32],"remains":[36],"equivalent":[37],"or":[39],"becomes":[40],"inequivalent":[41,71],"original":[44],"one":[45],"when":[46,72,77],"mass":[48],"and/or":[49],"potential":[50],"are":[51,70,80],"changed.":[52],"This":[53,101],"reduced":[56],"study":[59],"Schr\u00f6dinger":[61],"operators.":[62],"It":[63],"turns":[64],"out":[65],"that":[66,108],"representations":[69],"masses":[74,79],"differ.":[75],"Moreover,":[76],"same,":[82],"transition":[84],"between":[85,98],"equivalence":[86],"and":[87],"inequivalence":[88],"occurs":[89],"at":[90],"decay":[92,105],"rate":[93,106],"$-3/2$":[94],"difference":[97],"potentials.":[100],"contrasts":[102],"with":[103],"$-1$":[107],"defines":[109],"short-range":[111],"condition":[112],"in":[113],"scattering":[114],"theory.":[115]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}
