{"id":"https://openalex.org/W7214780740","doi":"https://doi.org/10.48550/arxiv.2609.34980","title":"A renormalized Lee Model: resolvent and spectral analysis","display_name":"A renormalized Lee Model: resolvent and spectral analysis","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214780740","doi":"https://doi.org/10.48550/arxiv.2609.34980"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34980","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34980","pdf_url":"https://arxiv.org/pdf/2609.34980","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/2609.34980","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047568596","display_name":"Claudio Cacciapuoti","orcid":"https://orcid.org/0000-0002-7256-4265","observed_orcids":["https://orcid.org/0000-0002-7256-4265"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cacciapuoti, Claudio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007328086","display_name":"Federica Muscolino","orcid":"https://orcid.org/0000-0002-7013-3760","observed_orcids":["https://orcid.org/0000-0002-7013-3760"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muscolino, Federica","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087670599","display_name":"Diego Noja","orcid":"https://orcid.org/0000-0003-1949-9369","observed_orcids":["https://orcid.org/0000-0003-1949-9369"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Noja, Diego","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034542231","display_name":"Andrea Posilicano","orcid":"https://orcid.org/0000-0002-9273-1892","observed_orcids":["https://orcid.org/0000-0002-9273-1892"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Posilicano, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.00019999999494757503,"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/T10899","display_name":"Advanced Operator Algebra Research","score":9.999999747378752e-05,"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/lee-model","display_name":"Lee model","score":0.8870000243186951},{"id":"https://openalex.org/keywords/renormalized-hamiltonian","display_name":"renormalized Hamiltonian","score":0.9160000085830688},{"id":"https://openalex.org/keywords/essential-spectrum","display_name":"essential spectrum","score":0.7570000290870667},{"id":"https://openalex.org/keywords/point-spectrum","display_name":"point spectrum","score":0.6439999938011169},{"id":"https://openalex.org/keywords/bound-states","display_name":"bound states","score":0.6449999809265137},{"id":"https://openalex.org/keywords/massive-bosons","display_name":"massive bosons","score":0.46299999952316284},{"id":"https://openalex.org/keywords/three-dimensional-field-theory","display_name":"three-dimensional field theory","score":0.6069999933242798},{"id":"https://openalex.org/keywords/operator-pencils","display_name":"operator pencils","score":0.3199999928474426}],"concepts":[{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.758899986743927},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.718500018119812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6585999727249146},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6243000030517578},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4668999910354614},{"id":"https://openalex.org/C81571819","wikidata":"https://www.wikidata.org/wiki/Q1426722","display_name":"Resolvent formalism","level":4,"score":0.46389999985694885},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.4546000063419342},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.4334999918937683},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4239000082015991},{"id":"https://openalex.org/C166124518","wikidata":"https://www.wikidata.org/wiki/Q1047702","display_name":"Renormalization","level":2,"score":0.4189000129699707},{"id":"https://openalex.org/C79118098","wikidata":"https://www.wikidata.org/wiki/Q43101","display_name":"Boson","level":2,"score":0.41609999537467957},{"id":"https://openalex.org/C2780297109","wikidata":"https://www.wikidata.org/wiki/Q917390","display_name":"Essential spectrum","level":3,"score":0.41359999775886536},{"id":"https://openalex.org/C83581075","wikidata":"https://www.wikidata.org/wiki/Q1361503","display_name":"Excitation","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.39309999346733093},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.34619998931884766},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.310699999332428},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30399999022483826},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.2897000014781952},{"id":"https://openalex.org/C80845027","wikidata":"https://www.wikidata.org/wiki/Q15144062","display_name":"Continuous spectrum","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C186121230","wikidata":"https://www.wikidata.org/wiki/Q7575215","display_name":"Spectral theory of ordinary differential equations","level":5,"score":0.2824999988079071},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.26510000228881836},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2628999948501587},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34980","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34980","pdf_url":"https://arxiv.org/pdf/2609.34980","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.2609.34980","doi":"https://doi.org/10.48550/arxiv.2609.34980","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34980","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:2609.34980","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34980","pdf_url":"https://arxiv.org/pdf/2609.34980","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":[{"id":"https://openalex.org/G6010381268","display_name":null,"funder_award_id":"2022CHELC7","funder_id":"https://openalex.org/F7311471023","funder_display_name":"NextGenerationEU"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334080","display_name":"Gruppo Nazionale per la Fisica Matematica","ror":"https://ror.org/01d6bq278"},{"id":"https://openalex.org/F7311471023","display_name":"NextGenerationEU","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214780740.pdf","grobid_xml":"https://content.openalex.org/works/W7214780740.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1609870158","https://openalex.org/W1645409925","https://openalex.org/W2026396882","https://openalex.org/W2037582149","https://openalex.org/W2066018285","https://openalex.org/W2077213244","https://openalex.org/W2086331938","https://openalex.org/W2086703563","https://openalex.org/W2163746119","https://openalex.org/W2784798212","https://openalex.org/W2979317359","https://openalex.org/W3011570003","https://openalex.org/W3035808100","https://openalex.org/W3133925304","https://openalex.org/W3213697053","https://openalex.org/W4255574254","https://openalex.org/W4311735215","https://openalex.org/W4400264820","https://openalex.org/W7134828917","https://openalex.org/W7166663174"],"related_works":["https://openalex.org/W2173679198","https://openalex.org/W2037582149","https://openalex.org/W4311735215","https://openalex.org/W2965450931","https://openalex.org/W1985863720","https://openalex.org/W2077213244","https://openalex.org/W1974435029","https://openalex.org/W2092860245","https://openalex.org/W2007825844","https://openalex.org/W1982866262"],"abstract_inverted_index":{"We":[0,67],"construct":[1,68],"and":[2,27,80,158],"analyze":[3],"a":[4,28,47,73,124,175,182],"renormalized":[5,11,149],"three-dimensional":[6],"massive":[7],"Lee":[8],"model;":[9],"its":[10],"Hamiltonian":[12,45],"is":[13,94,121,151,166],"defined":[14],"intrinsically":[15],"through":[16],"an":[17,55,63,160],"abstract":[18],"construction":[19],"which":[20],"explicitly":[21],"provides":[22],"the":[23,34,39,43,51,60,82,85,91,97,109,114,148,155,169,179,187],"operator":[24,57],"domain,":[25],"action":[26],"Kre\\u\u0131n-like":[29],"resolvent":[30],"formula.":[31],"Conservation":[32],"of":[33,42,50,54,62,141,181],"total":[35],"excitation":[36,78],"number":[37],"reduces":[38],"spectral":[40,52],"analysis":[41],"full":[44,92],"to":[46],"sector-wise":[48,87],"study":[49],"profile":[53],"explicit":[56,103,161],"pencil,":[58],"playing":[59],"role":[61],"operator-valued":[64],"Weyl":[65],"function.":[66],"essential":[69],"spectrum":[70,116,143],"components":[71],"in":[72,84,96,105,117,186],"sector":[74,120,132],"generated":[75],"by":[76,123],"lower":[77],"sectors":[79,100],"obtain":[81],"inclusion":[83],"expected":[86],"HVZ":[88],"type":[89],"formula;":[90],"formula":[93],"proved":[95],"first":[98],"two":[99,136],"and,":[101],"under":[102,159],"conditions,":[104],"every":[106,118,131],"sector.":[107,189],"Below":[108],"free":[110],"or":[111],"one-excitation":[112],"threshold,":[113],"point":[115],"higher":[119],"described":[122],"bounded":[125],"self-adjoint":[126],"nonnegative":[127],"Birman--Schwinger":[128],"operator.":[129],"In":[130,168],"with":[133],"at":[134],"least":[135],"excitations":[137],"we":[138,172],"prove":[139],"absence":[140],"sub-threshold":[142],"for":[144,178],"arbitrary":[145],"coupling":[146],"when":[147,164],"gap":[150],"not":[152],"smaller":[153],"than":[154],"boson":[156],"mass,":[157],"weak-coupling":[162],"condition":[163,177],"it":[165],"smaller.":[167],"latter":[170],"case":[171],"also":[173],"derive":[174],"sufficient":[176],"existence":[180],"simple":[183],"bound":[184],"state":[185],"two-excitation":[188]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
