{"id":"https://openalex.org/W7204771293","doi":"https://doi.org/10.48550/arxiv.2608.28485","title":"Gauge invariance, collective modes, and the justification of normal-state subtraction in Dirac superconductors","display_name":"Gauge invariance, collective modes, and the justification of normal-state subtraction in Dirac superconductors","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204771293","doi":"https://doi.org/10.48550/arxiv.2608.28485"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28485","pdf_url":"https://arxiv.org/pdf/2608.28485","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.28485","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082188473","display_name":"Hiroshi Hayasaka","orcid":"https://orcid.org/0000-0001-5847-9948","observed_orcids":["https://orcid.org/0000-0001-5847-9948"]},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hayasaka, Hiroshi","raw_affiliation_strings":["Department of Information Science and Technology , Tokyo University of Science , Noda , Chiba 278-8510 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Science and Technology , Tokyo University of Science , Noda , Chiba 278-8510 , Japan","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082188473"],"corresponding_institution_ids":["https://openalex.org/I161296585"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9291999936103821,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9291999936103821,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T10657","display_name":"Topological Materials and Phenomena","score":0.04580000042915344,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11682","display_name":"Advanced Condensed Matter Physics","score":0.004999999888241291,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/gauge-invariance","display_name":"gauge invariance","score":0.9990000128746033},{"id":"https://openalex.org/keywords/collective-excitations","display_name":"collective excitations","score":0.8059999942779541},{"id":"https://openalex.org/keywords/ward-identities","display_name":"Ward identities","score":0.6779999732971191},{"id":"https://openalex.org/keywords/vertex-corrections","display_name":"vertex corrections","score":0.8629999756813049},{"id":"https://openalex.org/keywords/electromagnetic-response","display_name":"electromagnetic response","score":0.6489999890327454},{"id":"https://openalex.org/keywords/bethe-salpeter-equation","display_name":"Bethe-Salpeter equation","score":0.8949999809265137},{"id":"https://openalex.org/keywords/s-wave-pairing","display_name":"s-wave pairing","score":0.871999979019165},{"id":"https://openalex.org/keywords/uv-regularization","display_name":"UV regularization","score":0.7910000085830688},{"id":"https://openalex.org/keywords/longitudinal-response","display_name":"longitudinal response","score":0.5529999732971191},{"id":"https://openalex.org/keywords/transverse-response","display_name":"transverse response","score":0.6480000019073486},{"id":"https://openalex.org/keywords/long-wavelength-approximation","display_name":"long-wavelength limit","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.718999981880188},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5802000164985657},{"id":"https://openalex.org/C2776590265","wikidata":"https://www.wikidata.org/wiki/Q5277275","display_name":"Dimensional regularization","level":3,"score":0.5514000058174133},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.517300009727478},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48429998755455017},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.46299999952316284},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.4562000036239624},{"id":"https://openalex.org/C52233224","wikidata":"https://www.wikidata.org/wiki/Q44363","display_name":"Fermion","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4104999899864197},{"id":"https://openalex.org/C10874694","wikidata":"https://www.wikidata.org/wiki/Q220620","display_name":"Meissner effect","level":3,"score":0.40959998965263367},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40799999237060547},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4018000066280365},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.38510000705718994},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C79955541","wikidata":"https://www.wikidata.org/wiki/Q1348371","display_name":"Dirac fermion","level":3,"score":0.3573000133037567},{"id":"https://openalex.org/C40263606","wikidata":"https://www.wikidata.org/wiki/Q105580","display_name":"Gauge boson","level":3,"score":0.33329999446868896},{"id":"https://openalex.org/C157470216","wikidata":"https://www.wikidata.org/wiki/Q7922778","display_name":"Vertex function","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.3253999948501587},{"id":"https://openalex.org/C149773537","wikidata":"https://www.wikidata.org/wiki/Q12969754","display_name":"Electromagnetic radiation","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C196258919","wikidata":"https://www.wikidata.org/wiki/Q1203816","display_name":"Lorenz gauge condition","level":5,"score":0.3160000145435333},{"id":"https://openalex.org/C166124518","wikidata":"https://www.wikidata.org/wiki/Q1047702","display_name":"Renormalization","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C68060419","wikidata":"https://www.wikidata.org/wiki/Q40754","display_name":"Subtraction","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C147247565","wikidata":"https://www.wikidata.org/wiki/Q5527635","display_name":"Gauge symmetry","level":3,"score":0.2709999978542328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26980000734329224},{"id":"https://openalex.org/C31593994","wikidata":"https://www.wikidata.org/wiki/Q832289","display_name":"Gauge fixing","level":4,"score":0.26409998536109924},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.25369998812675476},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2531000077724457},{"id":"https://openalex.org/C65211518","wikidata":"https://www.wikidata.org/wiki/Q16743426","display_name":"Introduction to gauge theory","level":3,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28485","pdf_url":"https://arxiv.org/pdf/2608.28485","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.28485","doi":"https://doi.org/10.48550/arxiv.2608.28485","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28485","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":"pmh:oai:arXiv.org:2608.28485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28485","pdf_url":"https://arxiv.org/pdf/2608.28485","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204771293.pdf","grobid_xml":"https://content.openalex.org/works/W7204771293.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2806491682","https://openalex.org/W2273479876","https://openalex.org/W4404307067","https://openalex.org/W4406793806","https://openalex.org/W2913017432","https://openalex.org/W1979646457","https://openalex.org/W1965850850","https://openalex.org/W1510632963","https://openalex.org/W2148057729","https://openalex.org/W310307993"],"abstract_inverted_index":{"In":[0,73,135],"Dirac":[1,8],"superconductors,":[2],"the":[3,23,35,41,49,59,62,67,87,95,100,104,111,115,120,127,137,141,146,151,160,168,184,188,193],"unbounded":[4],"spectrum":[5],"of":[6,61,140,170],"low-energy":[7],"models":[9],"is":[10,38],"known":[11],"to":[12,15,22,103,192],"give":[13],"rise":[14],"unphysical":[16],"interband":[17],"contributions":[18],"from":[19,40,159],"deep-lying":[20],"states":[21],"electromagnetic":[24,56,88,105],"response.":[25],"To":[26],"eliminate":[27],"these":[28],"contributions,":[29],"normal-state":[30,36],"subtraction":[31],"(NSS),":[32],"in":[33,110,145,187],"which":[34],"response":[37,89,123,130,163],"subtracted":[39],"superconducting-state":[42],"response,":[43,57],"has":[44,70],"been":[45],"widely":[46],"employed.":[47],"However,":[48],"relation":[50],"between":[51],"NSS":[52],"and":[53,84,98,172],"a":[54,78,202],"gauge-invariant":[55,152],"particularly":[58],"role":[60],"vertex":[63,116,142],"correction":[64,117,143],"required":[65,131],"by":[66,93,132,196],"Ward":[68],"identity,":[69],"remained":[71],"unclear.":[72],"this":[74],"work,":[75],"we":[76,177],"consider":[77],"massive-Dirac":[79],"model":[80],"with":[81,124,156,164],"$s$-wave":[82],"pairing":[83],"analytically":[85],"investigate":[86],"at":[90],"zero":[91],"temperature":[92],"solving":[94],"Bethe--Salpeter":[96],"equation":[97],"incorporating":[99],"collective-mode":[101],"contribution":[102],"vertex.":[106],"We":[107],"show":[108,178],"that,":[109],"static":[112,189],"long-wavelength":[113,147,190],"limit,":[114,148],"exactly":[118],"cancels":[119],"bare":[121,161],"longitudinal":[122,129],"NSS,":[125],"yielding":[126],"vanishing":[128],"gauge":[133,180],"invariance.":[134],"contrast,":[136],"transverse":[138,162],"component":[139],"vanishes":[144],"so":[149],"that":[150,157,179],"Meissner":[153],"weight":[154],"coincides":[155],"obtained":[158],"NSS.":[165,197,206],"Moreover,":[166],"within":[167],"class":[169],"isotropic":[171],"analytic":[173],"UV":[174],"regularization":[175,185],"terms,":[176],"invariance":[181],"uniquely":[182],"fixes":[183],"term":[186],"limit":[191],"value":[194],"prescribed":[195],"Our":[198],"results":[199],"thus":[200],"provide":[201],"microscopic":[203],"justification":[204],"for":[205]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-01T00:00:00"}