{"id":"https://openalex.org/W3184880576","doi":"https://doi.org/10.3390/sym13081373","title":"Iterants, Majorana Fermions and the Majorana-Dirac Equation","display_name":"Iterants, Majorana Fermions and the Majorana-Dirac Equation","publication_year":2021,"publication_date":"2021-07-28","ids":{"openalex":"https://openalex.org/W3184880576","doi":"https://doi.org/10.3390/sym13081373","mag":"3184880576"},"language":"en","primary_location":{"id":"doi:10.3390/sym13081373","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081373","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1373/pdf?version=1627466752","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/2073-8994/13/8/1373/pdf?version=1627466752","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057018104","display_name":"Louis H. Kauffman","orcid":"https://orcid.org/0000-0003-4135-8685"},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]},{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["RU","US"],"is_corresponding":true,"raw_author_name":"Louis H. Kauffman","raw_affiliation_strings":["Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA","Department of Mechanics and Mathematics, Novosibirsk State University, 630090 Novosibirsk, Russia"],"raw_orcid":"https://orcid.org/0000-0003-4135-8685","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USA","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"Department of Mechanics and Mathematics, Novosibirsk State University, 630090 Novosibirsk, Russia","institution_ids":["https://openalex.org/I188973947"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057018104"],"corresponding_institution_ids":["https://openalex.org/I188973947","https://openalex.org/I39422238"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08925934,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"8","first_page":"1373","last_page":"1373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10657","display_name":"Topological Materials and Phenomena","score":0.9993000030517578,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.9993000030517578,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9962000250816345,"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/majorana-equation","display_name":"Majorana equation","score":0.9004219770431519},{"id":"https://openalex.org/keywords/majorana","display_name":"MAJORANA","score":0.871202826499939},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.6771941184997559},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.591410756111145},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.5616677403450012},{"id":"https://openalex.org/keywords/fermion","display_name":"Fermion","score":0.5105413198471069},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.4783180058002472},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4721120595932007},{"id":"https://openalex.org/keywords/dirac-fermion","display_name":"Dirac fermion","score":0.46680739521980286},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4542832374572754},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.44474586844444275},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43960049748420715},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4129871726036072},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4120848476886749},{"id":"https://openalex.org/keywords/neutrino","display_name":"Neutrino","score":0.28078681230545044},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2682547867298126},{"id":"https://openalex.org/keywords/dirac-sea","display_name":"Dirac sea","score":0.1019490659236908}],"concepts":[{"id":"https://openalex.org/C45969854","wikidata":"https://www.wikidata.org/wiki/Q2727849","display_name":"Majorana equation","level":5,"score":0.9004219770431519},{"id":"https://openalex.org/C2778761060","wikidata":"https://www.wikidata.org/wiki/Q6714234","display_name":"MAJORANA","level":3,"score":0.871202826499939},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.6771941184997559},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.591410756111145},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.5616677403450012},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.5105413198471069},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.4783180058002472},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4721120595932007},{"id":"https://openalex.org/C79955541","wikidata":"https://www.wikidata.org/wiki/Q1348371","display_name":"Dirac fermion","level":3,"score":0.46680739521980286},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4542832374572754},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.44474586844444275},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43960049748420715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4129871726036072},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4120848476886749},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.28078681230545044},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2682547867298126},{"id":"https://openalex.org/C50575695","wikidata":"https://www.wikidata.org/wiki/Q1227393","display_name":"Dirac sea","level":4,"score":0.1019490659236908},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13081373","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081373","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1373/pdf?version=1627466752","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:doaj.org/article:4c0d8cabd5d543c99346a0ff7b2fe0d4","is_oa":true,"landing_page_url":"https://doaj.org/article/4c0d8cabd5d543c99346a0ff7b2fe0d4","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 13, Iss 8, p 1373 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/8/1373/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13081373","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13081373","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081373","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1373/pdf?version=1627466752","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5899999737739563}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3184880576.pdf","grobid_xml":"https://content.openalex.org/works/W3184880576.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W24586604","https://openalex.org/W580263262","https://openalex.org/W1487836916","https://openalex.org/W1552736770","https://openalex.org/W1560777125","https://openalex.org/W1648560695","https://openalex.org/W1973972788","https://openalex.org/W1986517262","https://openalex.org/W2001788988","https://openalex.org/W2011535253","https://openalex.org/W2025009334","https://openalex.org/W2036676626","https://openalex.org/W2046739675","https://openalex.org/W2135712311","https://openalex.org/W2141708961","https://openalex.org/W2153707409","https://openalex.org/W2417699198","https://openalex.org/W2765631112","https://openalex.org/W2956139510","https://openalex.org/W2963357794","https://openalex.org/W2977430961","https://openalex.org/W3084345044","https://openalex.org/W3102338691","https://openalex.org/W3103867809","https://openalex.org/W3104372980","https://openalex.org/W4232788318","https://openalex.org/W4234358158","https://openalex.org/W4234738784","https://openalex.org/W4236971238","https://openalex.org/W4239309077","https://openalex.org/W4247159043","https://openalex.org/W4255075412"],"related_works":["https://openalex.org/W2033776133","https://openalex.org/W2576248975","https://openalex.org/W2791625515","https://openalex.org/W4298696685","https://openalex.org/W2579545105","https://openalex.org/W4293775534","https://openalex.org/W2950841411","https://openalex.org/W2970682805","https://openalex.org/W3098039927","https://openalex.org/W2045589475"],"abstract_inverted_index":{"This":[0],"paper":[1,53],"explains":[2],"a":[3],"method":[4,74],"of":[5,12,24,57],"constructing":[6],"algebras,":[7],"starting":[8],"with":[9],"the":[10,44,55,58,61,65,72],"properties":[11],"discrimination":[13],"in":[14],"elementary":[15],"discrete":[16],"systems.":[17],"We":[18],"show":[19],"how":[20,37],"to":[21,29,43],"use":[22],"points":[23],"view":[25],"about":[26],"these":[27,38],"systems":[28],"construct":[30],"what":[31],"we":[32],"call":[33],"iterant":[34],"algebras":[35,39,48],"and":[36,49,64],"naturally":[40],"give":[41],"rise":[42],"complex":[45],"numbers,":[46],"Clifford":[47],"matrix":[50],"algebras.":[51],"The":[52],"discusses":[54],"structure":[56],"Schr\u00f6dinger":[59],"equation,":[60],"Dirac":[62,67],"equation":[63],"Majorana":[66],"equations,":[68],"finding":[69],"solutions":[70],"via":[71],"nilpotent":[73],"initiated":[75],"by":[76],"Peter":[77],"Rowlands.":[78]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
