{"id":"https://openalex.org/W2962990454","doi":"https://doi.org/10.1088/2399-6528/aaedcc","title":"On evidence for negative energies and masses in the Dirac equation through a unitary time-reversal operator","display_name":"On evidence for negative energies and masses in the Dirac equation through a unitary time-reversal operator","publication_year":2018,"publication_date":"2018-11-02","ids":{"openalex":"https://openalex.org/W2962990454","doi":"https://doi.org/10.1088/2399-6528/aaedcc","mag":"2962990454"},"language":"en","primary_location":{"id":"doi:10.1088/2399-6528/aaedcc","doi":"https://doi.org/10.1088/2399-6528/aaedcc","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2399-6528/aaedcc","pdf_url":"https://iopscience.iop.org/article/10.1088/2399-6528/aaedcc/pdf","source":{"id":"https://openalex.org/S4210180840","display_name":"Journal of Physics Communications","issn_l":"2399-6528","issn":["2399-6528"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Physics Communications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://iopscience.iop.org/article/10.1088/2399-6528/aaedcc/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027149165","display_name":"N. Debergh","orcid":"https://orcid.org/0000-0003-3537-6289","observed_orcids":["https://orcid.org/0000-0003-3537-6289"]},"institutions":[{"id":"https://openalex.org/I4210129191","display_name":"Haute \u00c9cole Charlemagne","ror":"https://ror.org/03er55z68","country_code":"BE","type":"education","lineage":["https://openalex.org/I4210129191"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"N Debergh","raw_affiliation_strings":["Department of agronomy, Haute Ecole Charlemagne, 3, rue Saint-Victor, 4500 Huy, Belgium"],"raw_orcid":"https://orcid.org/0000-0003-3537-6289","affiliations":[{"raw_affiliation_string":"Department of agronomy, Haute Ecole Charlemagne, 3, rue Saint-Victor, 4500 Huy, Belgium","institution_ids":["https://openalex.org/I4210129191"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062110214","display_name":"Jean-Pierre Petit","orcid":"https://orcid.org/0000-0003-3141-8584","observed_orcids":["https://orcid.org/0000-0003-3141-8584","https://orcid.org/0000-0002-2171-2619"]},"institutions":[{"id":"https://openalex.org/I4210129191","display_name":"Haute \u00c9cole Charlemagne","ror":"https://ror.org/03er55z68","country_code":"BE","type":"education","lineage":["https://openalex.org/I4210129191"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"J-P Petit","raw_affiliation_strings":["Department of agronomy, Haute Ecole Charlemagne, 3, rue Saint-Victor, 4500 Huy, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of agronomy, Haute Ecole Charlemagne, 3, rue Saint-Victor, 4500 Huy, Belgium","institution_ids":["https://openalex.org/I4210129191"]}]},{"author_position":"last","author":{"id":null,"display_name":"G D\u2019Agostini","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210129191","display_name":"Haute \u00c9cole Charlemagne","ror":"https://ror.org/03er55z68","country_code":"BE","type":"education","lineage":["https://openalex.org/I4210129191"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"G D\u2019Agostini","raw_affiliation_strings":["Department of agronomy, Haute Ecole Charlemagne, 3, rue Saint-Victor, 4500 Huy, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of agronomy, Haute Ecole Charlemagne, 3, rue Saint-Victor, 4500 Huy, Belgium","institution_ids":["https://openalex.org/I4210129191"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027149165","https://openalex.org/A5062110214"],"corresponding_institution_ids":["https://openalex.org/I4210129191"],"apc_list":{"value":1880,"currency":"USD","value_usd":1880},"apc_paid":{"value":1880,"currency":"USD","value_usd":1880},"fwci":0.8301,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.70555363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"2","issue":"11","first_page":"115012","last_page":"115012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11683","display_name":"Quantum and Classical Electrodynamics","score":0.4059999883174896,"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/T11683","display_name":"Quantum and Classical Electrodynamics","score":0.4059999883174896,"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.28299999237060547,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T11960","display_name":"Relativity and Gravitational Theory","score":0.14749999344348907,"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/dirac-equation","display_name":"Dirac equation","score":0.9390000104904175},{"id":"https://openalex.org/keywords/negative-energy-states","display_name":"negative energy states","score":0.7960000038146973},{"id":"https://openalex.org/keywords/negative-mass","display_name":"negative mass","score":0.8550000190734863},{"id":"https://openalex.org/keywords/antiparticles","display_name":"antiparticles","score":0.7760000228881836},{"id":"https://openalex.org/keywords/relativistic-quantum-mechanics","display_name":"relativistic quantum mechanics","score":0.7919999957084656}],"concepts":[{"id":"https://openalex.org/C2779428274","wikidata":"https://www.wikidata.org/wiki/Q662636","display_name":"Negative energy","level":2,"score":0.8816549777984619},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.7688025236129761},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7436564564704895},{"id":"https://openalex.org/C50575695","wikidata":"https://www.wikidata.org/wiki/Q1227393","display_name":"Dirac sea","level":4,"score":0.6912380456924438},{"id":"https://openalex.org/C179371143","wikidata":"https://www.wikidata.org/wiki/Q2495534","display_name":"Unitary transformation","level":3,"score":0.6794286370277405},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6659706234931946},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.5711227059364319},{"id":"https://openalex.org/C57476683","wikidata":"https://www.wikidata.org/wiki/Q3332147","display_name":"Relativistic quantum mechanics","level":4,"score":0.5662415027618408},{"id":"https://openalex.org/C30005106","wikidata":"https://www.wikidata.org/wiki/Q7858689","display_name":"Two-body Dirac equations","level":3,"score":0.5533966422080994},{"id":"https://openalex.org/C82189318","wikidata":"https://www.wikidata.org/wiki/Q6987233","display_name":"Negative mass","level":2,"score":0.4950188994407654},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.49431872367858887},{"id":"https://openalex.org/C79955541","wikidata":"https://www.wikidata.org/wiki/Q1348371","display_name":"Dirac fermion","level":3,"score":0.47820401191711426},{"id":"https://openalex.org/C125867301","wikidata":"https://www.wikidata.org/wiki/Q18205881","display_name":"Causal fermion system","level":5,"score":0.4644389748573303},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4557859003543854},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4440135657787323},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4292447865009308},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.41852355003356934},{"id":"https://openalex.org/C84076635","wikidata":"https://www.wikidata.org/wiki/Q5704918","display_name":"Helical Dirac fermion","level":5,"score":0.4112279415130615},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3690143823623657},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.35369873046875},{"id":"https://openalex.org/C194975256","wikidata":"https://www.wikidata.org/wiki/Q7269039","display_name":"Quantum dissipation","level":3,"score":0.1332990527153015},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.08195450901985168},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.07533428072929382},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1088/2399-6528/aaedcc","doi":"https://doi.org/10.1088/2399-6528/aaedcc","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2399-6528/aaedcc","pdf_url":"https://iopscience.iop.org/article/10.1088/2399-6528/aaedcc/pdf","source":{"id":"https://openalex.org/S4210180840","display_name":"Journal of Physics Communications","issn_l":"2399-6528","issn":["2399-6528"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Physics Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1809.05046","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.05046","pdf_url":"https://arxiv.org/pdf/1809.05046","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.1809.05046","doi":"https://doi.org/10.48550/arxiv.1809.05046","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1809.05046","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":"article-journal"},{"id":"doi:10.13140/rg.2.2.29710.00322","doi":"https://doi.org/10.13140/rg.2.2.29710.00322","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.29710.00322","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1088/2399-6528/aaedcc","doi":"https://doi.org/10.1088/2399-6528/aaedcc","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2399-6528/aaedcc","pdf_url":"https://iopscience.iop.org/article/10.1088/2399-6528/aaedcc/pdf","source":{"id":"https://openalex.org/S4210180840","display_name":"Journal of Physics Communications","issn_l":"2399-6528","issn":["2399-6528"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","norway-1","oarl","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Physics Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962990454.pdf","grobid_xml":"https://content.openalex.org/works/W2962990454.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W215993472","https://openalex.org/W1522763293","https://openalex.org/W1642827677","https://openalex.org/W1961633354","https://openalex.org/W1965075382","https://openalex.org/W1991711759","https://openalex.org/W1995233949","https://openalex.org/W1995841230","https://openalex.org/W2019157816","https://openalex.org/W2026198773","https://openalex.org/W2073832139","https://openalex.org/W2098669229","https://openalex.org/W2127865535","https://openalex.org/W2169521354","https://openalex.org/W2321245337","https://openalex.org/W2521284916","https://openalex.org/W2566726418","https://openalex.org/W2793263580","https://openalex.org/W2805205500","https://openalex.org/W3143815958","https://openalex.org/W4242039097"],"related_works":["https://openalex.org/W1582566253","https://openalex.org/W4220826753","https://openalex.org/W6959809779","https://openalex.org/W2612163037","https://openalex.org/W944240986","https://openalex.org/W794729608","https://openalex.org/W6893201955","https://openalex.org/W80532435","https://openalex.org/W1988153980","https://openalex.org/W1927898632"],"abstract_inverted_index":{"We":[0,19],"review":[1],"the":[2,10,14,27],"standards":[3],"of":[4,16],"relativistic":[5],"quantum":[6],"mechanics":[7],"such":[8],"as":[9],"Dirac":[11],"equation":[12],"under":[13],"concept":[15],"negative":[17,22],"masses.":[18],"show":[20],"that":[21],"energies":[23],"are":[24,29,37],"acceptable":[25],"provided":[26],"masses":[28],"simultaneously":[30],"negative.":[31],"Negative":[32],"energy":[33,41],"and":[34,42],"mass":[35,43],"anti-fermions":[36],"obtained":[38],"from":[39],"positive":[40],"fermions":[44],"through":[45],"a":[46],"unitary":[47],"PT":[48],"transformation.":[49]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-07-30T00:00:00"}
