{"id":"https://openalex.org/W7115697286","doi":"https://doi.org/10.1007/s00023-026-01778-w","title":"On the Spectrum of the Magnetic Dirac Operator","display_name":"On the Spectrum of the Magnetic Dirac Operator","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7115697286","doi":"https://doi.org/10.1007/s00023-026-01778-w"},"language":"en","primary_location":{"id":"doi:10.1007/s00023-026-01778-w","doi":"https://doi.org/10.1007/s00023-026-01778-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00023-026-01778-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00023-026-01778-w.pdf","source":{"id":"https://openalex.org/S27783554","display_name":"Annales Henri Poincar\u00e9","issn_l":"1424-0637","issn":["1424-0637","1424-0661"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales Henri Poincar\u00e9","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00023-026-01778-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Volker Branding","orcid":"https://orcid.org/0000-0002-1535-1474","observed_orcids":["https://orcid.org/0000-0002-1535-1474"]},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Volker Branding","raw_affiliation_strings":["Institute of Mathematics, University of Rostock, Ulmenstra\u00dfe 69, 18057, Rostock, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1535-1474","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Rostock, Ulmenstra\u00dfe 69, 18057, Rostock, Germany","institution_ids":["https://openalex.org/I4665924"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Nicolas Ginoux","orcid":null,"observed_orcids":[]},"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/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Ginoux","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CNRS, IECL, F-57000, Metz, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, IECL, F-57000, Metz, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I3017839442","https://openalex.org/I90183372"]}]},{"author_position":"last","author":{"id":null,"display_name":"Georges Habib","orcid":null,"observed_orcids":[]},"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/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR","LB"],"is_corresponding":false,"raw_author_name":"Georges Habib","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences II, Lebanese University, 90656 , Fanar-Matn, Lebanon","Universit\u00e9 de Lorraine, CNRS, IECL, F-54506, Nancy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences II, Lebanese University, 90656 , Fanar-Matn, Lebanon","institution_ids":["https://openalex.org/I160368002"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, IECL, F-54506, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I3017839442","https://openalex.org/I90183372"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4665924"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15756015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.9990000128746033,"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":0.9990000128746033,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.00019999999494757503,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spectrum","display_name":"spectrum","score":0.753000020980835},{"id":"https://openalex.org/keywords/eigenvalue-bounds","display_name":"eigenvalue bounds","score":0.9779999852180481},{"id":"https://openalex.org/keywords/closed-riemannian-manifolds","display_name":"closed Riemannian manifolds","score":0.9620000123977661},{"id":"https://openalex.org/keywords/flat-torus","display_name":"flat torus","score":0.925000011920929},{"id":"https://openalex.org/keywords/charged-particle-in-magnetic-field","display_name":"charged particle in magnetic field","score":0.8050000071525574},{"id":"https://openalex.org/keywords/relativistic-quantum-mechanics","display_name":"relativistic quantum mechanics","score":0.7229999899864197}],"concepts":[{"id":"https://openalex.org/C158650840","wikidata":"https://www.wikidata.org/wiki/Q907439","display_name":"Dirac operator","level":2,"score":0.7588000297546387},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5968999862670898},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5953999757766724},{"id":"https://openalex.org/C162475051","wikidata":"https://www.wikidata.org/wiki/Q692457","display_name":"Momentum operator","level":5,"score":0.5769000053405762},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5576000213623047},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.5351999998092651},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5246000289916992},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.4975999891757965},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4794999957084656},{"id":"https://openalex.org/C189686092","wikidata":"https://www.wikidata.org/wiki/Q903835","display_name":"Position operator","level":5,"score":0.40209999680519104},{"id":"https://openalex.org/C134440745","wikidata":"https://www.wikidata.org/wiki/Q1186765","display_name":"Ladder operator","level":4,"score":0.39329999685287476},{"id":"https://openalex.org/C50953366","wikidata":"https://www.wikidata.org/wiki/Q385599","display_name":"Dirac comb","level":5,"score":0.3896999955177307},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.37299999594688416},{"id":"https://openalex.org/C177547823","wikidata":"https://www.wikidata.org/wiki/Q5133083","display_name":"Clifford analysis","level":3,"score":0.34450000524520874},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33379998803138733},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.32510000467300415},{"id":"https://openalex.org/C73052347","wikidata":"https://www.wikidata.org/wiki/Q5282616","display_name":"Displacement operator","level":5,"score":0.32089999318122864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31439998745918274},{"id":"https://openalex.org/C149545384","wikidata":"https://www.wikidata.org/wiki/Q5280160","display_name":"Dirac algebra","level":3,"score":0.31349998712539673},{"id":"https://openalex.org/C51021465","wikidata":"https://www.wikidata.org/wiki/Q7575181","display_name":"Spectral asymmetry","level":4,"score":0.29840001463890076},{"id":"https://openalex.org/C156785651","wikidata":"https://www.wikidata.org/wiki/Q688945","display_name":"Dirac spinor","level":4,"score":0.29739999771118164},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.29649999737739563},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.28439998626708984}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00023-026-01778-w","doi":"https://doi.org/10.1007/s00023-026-01778-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00023-026-01778-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00023-026-01778-w.pdf","source":{"id":"https://openalex.org/S27783554","display_name":"Annales Henri Poincar\u00e9","issn_l":"1424-0637","issn":["1424-0637","1424-0661"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales Henri Poincar\u00e9","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2512.13338","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.13338","pdf_url":"https://arxiv.org/pdf/2512.13338","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05415814v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05415814v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2025","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2512.13338","doi":"https://doi.org/10.48550/arxiv.2512.13338","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.13338","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":"doi:10.1007/s00023-026-01778-w","doi":"https://doi.org/10.1007/s00023-026-01778-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00023-026-01778-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00023-026-01778-w.pdf","source":{"id":"https://openalex.org/S27783554","display_name":"Annales Henri Poincar\u00e9","issn_l":"1424-0637","issn":["1424-0637","1424-0661"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales Henri Poincar\u00e9","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310925","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7115697286.pdf","grobid_xml":"https://content.openalex.org/works/W7115697286.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4390112246","https://openalex.org/W4213330757","https://openalex.org/W7009763485","https://openalex.org/W7120706023","https://openalex.org/W3023532688","https://openalex.org/W4405293902","https://openalex.org/W6992412803","https://openalex.org/W2516877277","https://openalex.org/W2058972126","https://openalex.org/W3042465726"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"magnetic":[2,15,56,73],"Dirac":[3,57],"operator":[4,19,58],"describes":[5],"the":[6,55,72,76,81],"relativistic":[7],"motion":[8],"of":[9,23,28,51,71],"a":[10,14,21,38,49],"charged":[11],"particle":[12],"in":[13,25],"field.":[16],"Although":[17],"this":[18,42,45],"got":[20],"lot":[22],"attention":[24],"physics,":[26],"many":[27],"its":[29,66],"fundamental":[30],"mathematical":[31],"properties":[32],"remain":[33],"unexplored.":[34],"This":[35],"article":[36],"constitutes":[37],"step":[39],"toward":[40],"filling":[41],"gap.":[43],"To":[44],"end,":[46],"we":[47],"provide":[48],"number":[50],"eigenvalue":[52],"estimates":[53],"for":[54,68],"on":[59,75,80],"closed":[60],"Riemannian":[61],"manifolds":[62],"and":[63,79],"explicitly":[64],"compute":[65],"spectrum":[67],"specific":[69],"choices":[70],"field":[74],"flat":[77],"torus":[78],"three-dimensional":[82],"round":[83],"sphere.":[84]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2025-12-17T00:00:00"}