{"id":"https://openalex.org/W4283528059","doi":"https://doi.org/10.1515/zna-2022-0018","title":"The generation of mass in a non-linear field theory","display_name":"The generation of mass in a non-linear field theory","publication_year":2022,"publication_date":"2022-06-24","ids":{"openalex":"https://openalex.org/W4283528059","doi":"https://doi.org/10.1515/zna-2022-0018"},"language":"en","primary_location":{"id":"doi:10.1515/zna-2022-0018","doi":"https://doi.org/10.1515/zna-2022-0018","is_oa":false,"landing_page_url":"https://doi.org/10.1515/zna-2022-0018","pdf_url":null,"source":{"id":"https://openalex.org/S4210168924","display_name":"Zeitschrift f\u00fcr Naturforschung A","issn_l":"0340-4811","issn":["0340-4811","0932-0784","1865-7109"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Zeitschrift f\u00fcr Naturforschung A","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045155292","display_name":"Thomas Warmann","orcid":"https://orcid.org/0000-0001-6814-755X","observed_orcids":["https://orcid.org/0000-0001-6814-755X"]},"institutions":[{"id":"https://openalex.org/I4210127368","display_name":"Sopra (France)","ror":"https://ror.org/02mhjkx12","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210127368"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Thomas Warmann","raw_affiliation_strings":["Sopra Steria SA , Hans-Henny-Jahnn-Weg 29 , Hamburg 22085 , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sopra Steria SA , Hans-Henny-Jahnn-Weg 29 , Hamburg 22085 , Germany","institution_ids":["https://openalex.org/I4210127368"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045155292"],"corresponding_institution_ids":["https://openalex.org/I4210127368"],"apc_list":{"value":2000,"currency":"EUR","value_usd":2107},"apc_paid":null,"fwci":0.2909,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.42336456,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"77","issue":"8","first_page":"723","last_page":"798"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.6557999849319458,"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"}},"topics":[{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.6557999849319458,"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"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.16869999468326569,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.15770000219345093,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/particle-mass-spectrum","display_name":"particle mass spectrum","score":0.8029999732971191},{"id":"https://openalex.org/keywords/nonlinear-field-theory","display_name":"nonlinear field theory","score":0.8199999928474426},{"id":"https://openalex.org/keywords/mass-hierarchy","display_name":"mass hierarchy","score":0.656000018119812},{"id":"https://openalex.org/keywords/fine-structure-constant","display_name":"fine-structure constant","score":0.949999988079071},{"id":"https://openalex.org/keywords/electron-mass","display_name":"electron mass","score":0.48100000619888306},{"id":"https://openalex.org/keywords/self-similarity","display_name":"self-similarity","score":0.7210000157356262},{"id":"https://openalex.org/keywords/einstein-field-equations","display_name":"Einstein field equations","score":0.5960000157356262}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6078218221664429},{"id":"https://openalex.org/C15580451","wikidata":"https://www.wikidata.org/wiki/Q3077640","display_name":"Mass formula","level":2,"score":0.5689311623573303},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5459200739860535},{"id":"https://openalex.org/C29058008","wikidata":"https://www.wikidata.org/wiki/Q1326936","display_name":"Electromagnetic mass","level":2,"score":0.5086715817451477},{"id":"https://openalex.org/C177905867","wikidata":"https://www.wikidata.org/wiki/Q3840065","display_name":"Atomic mass","level":2,"score":0.5015590190887451},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.487270712852478},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.46468591690063477},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.45390474796295166},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.4319651126861572},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.4185221493244171},{"id":"https://openalex.org/C179764930","wikidata":"https://www.wikidata.org/wiki/Q3509437","display_name":"Effective mass (spring\u2013mass system)","level":2,"score":0.4141387939453125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2832931876182556},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.2827364206314087},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.20283690094947815},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12914732098579407},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/zna-2022-0018","doi":"https://doi.org/10.1515/zna-2022-0018","is_oa":false,"landing_page_url":"https://doi.org/10.1515/zna-2022-0018","pdf_url":null,"source":{"id":"https://openalex.org/S4210168924","display_name":"Zeitschrift f\u00fcr Naturforschung A","issn_l":"0340-4811","issn":["0340-4811","0932-0784","1865-7109"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Zeitschrift f\u00fcr Naturforschung A","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W116081247","https://openalex.org/W1537758379","https://openalex.org/W1548369026","https://openalex.org/W1551991956","https://openalex.org/W1566634837","https://openalex.org/W1662706126","https://openalex.org/W1674463658","https://openalex.org/W1688317938","https://openalex.org/W1808881618","https://openalex.org/W1914726000","https://openalex.org/W1965682166","https://openalex.org/W1968431963","https://openalex.org/W1969940388","https://openalex.org/W1973460784","https://openalex.org/W1986337070","https://openalex.org/W1989736751","https://openalex.org/W2001054501","https://openalex.org/W2001666312","https://openalex.org/W2006970299","https://openalex.org/W2009817576","https://openalex.org/W2013488309","https://openalex.org/W2015610852","https://openalex.org/W2028737088","https://openalex.org/W2030274362","https://openalex.org/W2037087349","https://openalex.org/W2043669277","https://openalex.org/W2046134233","https://openalex.org/W2048791021","https://openalex.org/W2061031824","https://openalex.org/W2080657333","https://openalex.org/W2081523432","https://openalex.org/W2082739523","https://openalex.org/W2112604408","https://openalex.org/W2114287606","https://openalex.org/W2120334388","https://openalex.org/W2133739599","https://openalex.org/W2149826827","https://openalex.org/W2167477747","https://openalex.org/W2175272295","https://openalex.org/W2229076839","https://openalex.org/W2312681568","https://openalex.org/W2326323934","https://openalex.org/W2490850203","https://openalex.org/W2556107557","https://openalex.org/W2611409506","https://openalex.org/W2612938853","https://openalex.org/W2886898130","https://openalex.org/W2936429489","https://openalex.org/W2987209375","https://openalex.org/W3108284800","https://openalex.org/W3153059789","https://openalex.org/W4233060462","https://openalex.org/W6681074977","https://openalex.org/W7096684903"],"related_works":["https://openalex.org/W2922047323","https://openalex.org/W2963358068","https://openalex.org/W2963391610","https://openalex.org/W998854520","https://openalex.org/W2913574306","https://openalex.org/W2962217287","https://openalex.org/W586944865","https://openalex.org/W2965915937","https://openalex.org/W4416068889","https://openalex.org/W4411466478"],"abstract_inverted_index":{"Abstract":[0],"The":[1,38,60,129],"mass":[2,62,83,92,103,163],"spectrum":[3],"of":[4,40,58,101,112,140,155,171],"elementary":[5],"particles":[6],"is":[7,85,106],"calculated":[8,61,162],"in":[9,22,34,50,65,120],"a":[10,23,51,55,146],"new":[11],"approach,":[12],"based":[13],"on":[14,79],"B.":[15],"Heim\u2019s":[16],"quantum":[17,158],"field":[18,32],"theory,":[19],"which":[20],"manifests":[21],"non-linear":[24,150],"eigenvalue":[25],"equation":[26,33],"and":[27,45,93,125],"merges":[28],"into":[29],"the":[30,35,41,70,82,88,94,99,109,113,118,123,126,137,141,156,161,168],"Einstein":[31],"macroscopic":[36],"limit.":[37],"poly-metric":[39],"theory":[42],"allows":[43],"spacetime":[44],"matter":[46],"to":[47,87,108,136,167],"be":[48],"described":[49],"unified":[52],"formalism,":[53],"representing":[54],"radical":[56],"geometrisation":[57],"physics.":[59],"energies":[63],"are":[64,133],"very":[66],"good":[67],"agreement":[68],"with":[69],"empirical":[71],"data":[72],"(error":[73],"<":[74],"1":[75],"%":[76],"${<":[77],"}1\\%$":[78],"average)":[80],"if":[81],"scale":[84],"gauged":[86],"electron":[89],"as":[90],"lowest":[91],"second":[95],"main":[96,157],"parameter,":[97],"determining":[98],"strength":[100,121],"obtained":[102,130],"hierarchy":[104,131],"levels,":[105],"close":[107],"half":[110],"inverse":[111],"fine":[114],"structure":[115],"constant,":[116],"describing":[117],"difference":[119],"between":[122],"electromagnetic":[124],"strong":[127],"interaction.":[128],"levels":[132],"not":[134],"identical":[135,166],"particle":[138],"generations":[139],"Standard":[142],"Model;":[143],"however,":[144],"show":[145],"self-similarity":[147],"typical":[148],"for":[149],"theories.":[151],"For":[152],"higher":[153],"values":[154],"number":[159],"N,":[160],"formula":[164],"becomes":[165],"phenomenological":[169],"formulae":[170],"Nambu,":[172],"respectively,":[173],"Mac":[174],"Gregor.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-06-27T00:00:00"}