{"id":"https://openalex.org/W2754358151","doi":"https://doi.org/10.3390/e19110575","title":"The Isolated Electron: De Broglie\u2019s Hidden Thermodynamics, SU(2) Quantum Yang-Mills Theory, and a Strongly Perturbed BPS Monopole","display_name":"The Isolated Electron: De Broglie\u2019s Hidden Thermodynamics, SU(2) Quantum Yang-Mills Theory, and a Strongly Perturbed BPS Monopole","publication_year":2017,"publication_date":"2017-10-26","ids":{"openalex":"https://openalex.org/W2754358151","doi":"https://doi.org/10.3390/e19110575","mag":"2754358151"},"language":"en","primary_location":{"id":"doi:10.3390/e19110575","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19110575","pdf_url":"https://www.mdpi.com/1099-4300/19/11/575/pdf?version=1509007662","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/11/575/pdf?version=1509007662","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ralf Hofmann","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ralf Hofmann","raw_affiliation_strings":["Institut f\u00fcr Photonenforschung und Synchrotronstrahlung, Karlsruher Institut f\u00fcr Technologie, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany","Institut f\u00fcr Theoretische Physik, Universit\u00e4t Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Photonenforschung und Synchrotronstrahlung, Karlsruher Institut f\u00fcr Technologie, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik, Universit\u00e4t Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany","institution_ids":["https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I102335020","https://openalex.org/I223822909"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3659,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.6432399,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"11","first_page":"575","last_page":"575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11683","display_name":"Quantum and Classical Electrodynamics","score":0.7846999764442444,"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":0.7846999764442444,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.04230000078678131,"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":0.015200000256299973,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/magnetic-monopole","display_name":"Magnetic monopole","score":0.7674999833106995},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5503000020980835},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5060999989509583},{"id":"https://openalex.org/keywords/electron","display_name":"Electron","score":0.45329999923706055},{"id":"https://openalex.org/keywords/coulomb","display_name":"Coulomb","score":0.4260999858379364},{"id":"https://openalex.org/keywords/classical-electron-radius","display_name":"Classical electron radius","score":0.41780000925064087},{"id":"https://openalex.org/keywords/lorentz-transformation","display_name":"Lorentz transformation","score":0.4016000032424927},{"id":"https://openalex.org/keywords/charge","display_name":"Charge (physics)","score":0.39899998903274536},{"id":"https://openalex.org/keywords/compton-wavelength","display_name":"Compton wavelength","score":0.3910999894142151},{"id":"https://openalex.org/keywords/wave-function","display_name":"Wave function","score":0.3831999897956848}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8827999830245972},{"id":"https://openalex.org/C149298590","wikidata":"https://www.wikidata.org/wiki/Q219708","display_name":"Magnetic monopole","level":2,"score":0.7674999833106995},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5503000020980835},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5060999989509583},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.5006999969482422},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.45329999923706055},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.4260999858379364},{"id":"https://openalex.org/C86855206","wikidata":"https://www.wikidata.org/wiki/Q2152581","display_name":"Classical electron radius","level":3,"score":0.41780000925064087},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.4016000032424927},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C144429999","wikidata":"https://www.wikidata.org/wiki/Q1145377","display_name":"Compton wavelength","level":4,"score":0.3910999894142151},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3882000148296356},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C37387333","wikidata":"https://www.wikidata.org/wiki/Q652571","display_name":"Bohr radius","level":3,"score":0.3562000095844269},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C40937832","wikidata":"https://www.wikidata.org/wiki/Q1111","display_name":"Electric charge","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C104240894","wikidata":"https://www.wikidata.org/wiki/Q867448","display_name":"Principal quantum number","level":4,"score":0.34540000557899475},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.3416999876499176},{"id":"https://openalex.org/C71993908","wikidata":"https://www.wikidata.org/wiki/Q1093427","display_name":"Lorentz covariance","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C11135259","wikidata":"https://www.wikidata.org/wiki/Q2477027","display_name":"Length scale","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C68030841","wikidata":"https://www.wikidata.org/wiki/Q172948","display_name":"Bohr model","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3010999858379364},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2809999883174896},{"id":"https://openalex.org/C128228380","wikidata":"https://www.wikidata.org/wiki/Q468999","display_name":"Planck mass","level":3,"score":0.27880001068115234},{"id":"https://openalex.org/C65494353","wikidata":"https://www.wikidata.org/wiki/Q180241","display_name":"Internal energy","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C141886431","wikidata":"https://www.wikidata.org/wiki/Q1193821","display_name":"Quantum fluctuation","level":3,"score":0.2685999870300293},{"id":"https://openalex.org/C151987854","wikidata":"https://www.wikidata.org/wiki/Q1097654","display_name":"Invariant mass","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C164866673","wikidata":"https://www.wikidata.org/wiki/Q304054","display_name":"Charge conservation","level":3,"score":0.25769999623298645}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e19110575","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19110575","pdf_url":"https://www.mdpi.com/1099-4300/19/11/575/pdf?version=1509007662","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.03873","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.03873","pdf_url":"https://arxiv.org/pdf/1709.03873","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:doaj.org/article:857d8aa735fe4900b8f643c1c06ddff0","is_oa":true,"landing_page_url":"https://doaj.org/article/857d8aa735fe4900b8f643c1c06ddff0","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":"Entropy, Vol 19, Iss 11, p 575 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/19/11/575/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e19110575","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":"Entropy; Volume 19; Issue 11; Pages: 575","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e19110575","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19110575","pdf_url":"https://www.mdpi.com/1099-4300/19/11/575/pdf?version=1509007662","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1507400589","https://openalex.org/W1607006092","https://openalex.org/W1696068948","https://openalex.org/W1703910647","https://openalex.org/W1805515744","https://openalex.org/W1862698929","https://openalex.org/W1974659638","https://openalex.org/W1989067717","https://openalex.org/W1993902660","https://openalex.org/W2011393113","https://openalex.org/W2013669657","https://openalex.org/W2021350329","https://openalex.org/W2027710569","https://openalex.org/W2035115555","https://openalex.org/W2037941549","https://openalex.org/W2044438425","https://openalex.org/W2046291902","https://openalex.org/W2059245145","https://openalex.org/W2060036385","https://openalex.org/W2060222759","https://openalex.org/W2067137320","https://openalex.org/W2070151728","https://openalex.org/W2076365797","https://openalex.org/W2080044952","https://openalex.org/W2080143633","https://openalex.org/W2081796865","https://openalex.org/W2083941350","https://openalex.org/W2085299414","https://openalex.org/W2086104596","https://openalex.org/W2104213222","https://openalex.org/W2107054201","https://openalex.org/W2127865535","https://openalex.org/W2135934849","https://openalex.org/W2157338954","https://openalex.org/W2225565636","https://openalex.org/W2230728100","https://openalex.org/W2232454336","https://openalex.org/W2335984944","https://openalex.org/W2734656033","https://openalex.org/W2735365941","https://openalex.org/W4231682458","https://openalex.org/W4236575607","https://openalex.org/W4245386860","https://openalex.org/W4253093627","https://openalex.org/W4254330616","https://openalex.org/W4300438285","https://openalex.org/W4302030582","https://openalex.org/W6634749355","https://openalex.org/W6641878197","https://openalex.org/W6655345361","https://openalex.org/W7027614512"],"related_works":[],"abstract_inverted_index":{"Based":[0],"on":[1,23,35,43],"a":[2,11,55,99,116,122,134],"recent":[3],"numerical":[4],"simulation":[5],"of":[6,10,28,31,74,80,101,104,126,142,176,189],"the":[7,24,29,39,44,50,69,81,95,110,143,169,173,177,184,187,190],"temporal":[8],"evolution":[9],"spherically":[12],"perturbed":[13,118],"BPS":[14,119],"monopole,":[15],"SU(2)":[16,63,146],"Yang-Mills":[17,65,147],"thermodynamics,":[18],"Louis":[19],"de":[20],"Broglie\u2019s":[21],"deliberations":[22],"disparate":[25],"Lorentz":[26],"transformations":[27],"frequency":[30],"an":[32],"internal":[33],"\u201cclock\u201d":[34],"one":[36],"hand":[37],"and":[38,47,145,183],"associated":[40],"quantum":[41],"energy":[42,195],"other":[45],"hand,":[46],"postulating":[48],"that":[49],"electron":[51,144,191],"is":[52,92,154,196],"represented":[53],"by":[54],"figure-eight":[56],"shaped,":[57],"self-intersecting":[58],"center":[59],"vortex":[60],"loop":[61],"in":[62,78,152],"Quantum":[64],"theory":[66],"we":[67],"estimate":[68],"spatial":[70],"radius":[71,171],"R":[72,161],"0":[73,107,141,162],"this":[75],"self-intersection":[76],"region":[77],"terms":[79],"electron\u2019s":[82],"Compton":[83],"wave":[84],"length":[85],"\u03bb":[86,180],"C":[87,181],".":[88,159],"This":[89],"region,":[90],"which":[91,151],"immersed":[93],"into":[94],"confining":[96],"phase,":[97],"constitutes":[98],"blob":[100],"deconfining":[102],"phase":[103],"temperature":[105,112],"T":[106,113,157],"mildly":[108],"above":[109],"critical":[111],"c":[114,158],"carrying":[115],"frequently":[117],"monopole":[120,178],"(with":[121],"magnetic-electric":[123],"dual":[124],"interpretation":[125],"its":[127],"charge":[128],"w.r.t.":[129],"U(1)\u2282SU(2)).":[130],"We":[131],"also":[132],"establish":[133],"quantitative":[135],"relation":[136],"between":[137],"rest":[138],"mass":[139,188],"m":[140],"scale":[148],"\u039b":[149],",":[150,182],"turn":[153],"defined":[155],"via":[156],"Surprisingly,":[160],"turns":[163],"out":[164],"to":[165,168,186,193],"be":[166],"comparable":[167],"Bohr":[170],"while":[172],"core":[174],"size":[175],"matches":[179],"correction":[185],"due":[192],"Coulomb":[194],"about":[197],"2%.":[198]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2017-09-25T00:00:00"}
