{"id":"https://openalex.org/W3030842570","doi":"https://doi.org/10.3390/sym12071121","title":"Charge Conjugation Symmetry in the Finite Basis Approximation of the Dirac Equation","display_name":"Charge Conjugation Symmetry in the Finite Basis Approximation of the Dirac Equation","publication_year":2020,"publication_date":"2020-07-06","ids":{"openalex":"https://openalex.org/W3030842570","doi":"https://doi.org/10.3390/sym12071121","mag":"3030842570"},"language":"en","primary_location":{"id":"doi:10.3390/sym12071121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071121","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1121/pdf","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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/7/1121/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088273145","display_name":"Maen Salman","orcid":"https://orcid.org/0000-0002-8214-9524"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I4210144120","display_name":"Laboratoire de Chimie et Physique Quantiques","ror":"https://ror.org/056g7f250","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210128300","https://openalex.org/I4210144120","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Maen Salman","raw_affiliation_strings":["Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS, Universit\u00e9 Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France","Groupe THEO (LCPQ)"],"raw_orcid":"https://orcid.org/0000-0002-8214-9524","affiliations":[{"raw_affiliation_string":"Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS, Universit\u00e9 Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I4210144120"]},{"raw_affiliation_string":"Groupe THEO (LCPQ)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084672632","display_name":"Trond Saue","orcid":"https://orcid.org/0000-0001-6407-0305"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I4210144120","display_name":"Laboratoire de Chimie et Physique Quantiques","ror":"https://ror.org/056g7f250","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210128300","https://openalex.org/I4210144120","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Trond Saue","raw_affiliation_strings":["Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS, Universit\u00e9 Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France","Groupe THEO (LCPQ)"],"raw_orcid":"https://orcid.org/0000-0001-6407-0305","affiliations":[{"raw_affiliation_string":"Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS, Universit\u00e9 Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I4210144120"]},{"raw_affiliation_string":"Groupe THEO (LCPQ)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084672632"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I4210144120"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.344,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.53583858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"7","first_page":"1121","last_page":"1121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10523","display_name":"Atomic and Molecular Physics","score":1.0,"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/T10523","display_name":"Atomic and Molecular Physics","score":1.0,"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/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9986000061035156,"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/T12579","display_name":"Muon and positron interactions and applications","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/charge","display_name":"Charge (physics)","score":0.705611526966095},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6930176019668579},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6106863617897034},{"id":"https://openalex.org/keywords/angular-momentum","display_name":"Angular momentum","score":0.6027212738990784},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.5786597728729248},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.5720932483673096},{"id":"https://openalex.org/keywords/wave-function","display_name":"Wave function","score":0.4772596061229706},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.46559131145477295},{"id":"https://openalex.org/keywords/quantum-electrodynamics","display_name":"Quantum electrodynamics","score":0.4579455256462097},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4262588620185852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.10726088285446167}],"concepts":[{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.705611526966095},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6930176019668579},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6106863617897034},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.6027212738990784},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.5786597728729248},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.5720932483673096},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.4772596061229706},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.46559131145477295},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.4579455256462097},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4262588620185852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.10726088285446167},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12071121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071121","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1121/pdf","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:HAL:hal-02957385v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02957385","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, 2020, 12 (7), pp.1121. ⟨10.3390/sym12071121⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:3e71bbfdb76d4507a3dacdf943fce4a0","is_oa":true,"landing_page_url":"https://doaj.org/article/3e71bbfdb76d4507a3dacdf943fce4a0","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 12, Iss 7, p 1121 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym12071121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071121","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1121/pdf","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":[{"display_name":"Affordable and clean energy","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G4972271647","display_name":null,"funder_award_id":"ANR-17-CE29-0004-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8604190413","display_name":"Molecular Quantum Electrodynamics","funder_award_id":"ANR-17-CE29-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W241891101","https://openalex.org/W1966987215","https://openalex.org/W1972497193","https://openalex.org/W1975124435","https://openalex.org/W1978941439","https://openalex.org/W1994253622","https://openalex.org/W2012130532","https://openalex.org/W2016058130","https://openalex.org/W2026350095","https://openalex.org/W2039878217","https://openalex.org/W2041928384","https://openalex.org/W2046013326","https://openalex.org/W2050259998","https://openalex.org/W2071353989","https://openalex.org/W2073500861","https://openalex.org/W2078958038","https://openalex.org/W2085329218","https://openalex.org/W2102522151","https://openalex.org/W2132548949","https://openalex.org/W2134769107","https://openalex.org/W2154699785","https://openalex.org/W2163398331","https://openalex.org/W2477140671","https://openalex.org/W2509334721","https://openalex.org/W3004369732","https://openalex.org/W4239748980","https://openalex.org/W6671959648","https://openalex.org/W6685541113","https://openalex.org/W6832037346"],"related_works":["https://openalex.org/W3143842500","https://openalex.org/W2034854043","https://openalex.org/W2066838737","https://openalex.org/W2148444155","https://openalex.org/W3145198003","https://openalex.org/W2027151972","https://openalex.org/W2033701889","https://openalex.org/W2020494338","https://openalex.org/W3002806525","https://openalex.org/W833423817"],"abstract_inverted_index":{"Four-component":[0],"relativistic":[1],"atomic":[2],"and":[3,34,75,91],"molecular":[4],"calculations":[5],"are":[6,16,71,190],"typically":[7],"performed":[8],"within":[9,60,88],"the":[10,46,53,61,89,109,114,124,134,137,151,158,182,207],"no-pair":[11],"approximation":[12],"where":[13,186],"negative-energy":[14],"solutions":[15,146,189,205],"discarded.":[17],"These":[18],"states":[19],"are,":[20],"however,":[21],"needed":[22],"in":[23,56,203,213],"QED":[24],"calculations,":[25],"wherein,":[26],"furthermore,":[27],"charge":[28,49,82,129,143,193],"conjugation":[29,50,83,130,144,194],"symmetry,":[30],"which":[31],"connects":[32],"electronic":[33],"positronic":[35],"solutions,":[36],"becomes":[37],"an":[38],"issue.":[39],"In":[40],"this":[41,156],"work,":[42],"we":[43,180],"shall":[44],"discuss":[45],"realization":[47],"of":[48,52,102,113,136,147,150,160,206,210,215],"symmetry":[51,84,131,202],"Dirac":[54,184],"equation":[55],"a":[57,99,177],"central":[58],"field":[59],"finite":[62],"basis":[63,68,103,139,161],"approximation.":[64],"Three":[65],"schemes":[66],"for":[67],"set":[69],"construction":[70],"considered:":[72],"restricted,":[73],"inverse,":[74],"dual":[76,118],"kinetic":[77,93,119],"balance.":[78],"We":[79,196],"find":[80],"that":[81,105,198,204],"can":[85],"be":[86],"realized":[87],"restricted":[90],"inverse":[92],"balance":[94,120],"prescriptions,":[95],"but":[96],"only":[97],"with":[98,128],"special":[100,178],"form":[101,135],"functions":[104],"does":[106],"not":[107],"obey":[108],"right":[110],"boundary":[111],"conditions":[112],"radial":[115,138],"wavefunctions.":[116],"The":[117],"prescription":[121],"is,":[122],"on":[123],"other":[125],"hand,":[126],"compatible":[127],"without":[132],"restricting":[133],"functions.":[140],"However,":[141],"since":[142],"relates":[145],"opposite":[148,187,216],"value":[149,209],"quantum":[152],"number":[153],"\u03ba":[154,211],",":[155],"requires":[157],"use":[159],"sets":[162],"chosen":[163],"according":[164],"to":[165],"total":[166],"angular":[167,173],"momentum":[168,174],"j":[169],"rather":[170],"than":[171],"orbital":[172],"\u2113.":[175],"As":[176],"case,":[179],"consider":[181],"free-particle":[183],"equation,":[185],"energy":[188],"related":[191],"by":[192],"symmetry.":[195],"show":[197],"there":[199],"is":[200],"additional":[201],"same":[208],"come":[212],"pairs":[214],"energy.":[217]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}