{"id":"https://openalex.org/W4319081346","doi":"https://doi.org/10.3390/sym15020414","title":"How to Determine the Branch Points of Correlation Functions in Euclidean Space II: Three-Point Functions","display_name":"How to Determine the Branch Points of Correlation Functions in Euclidean Space II: Three-Point Functions","publication_year":2023,"publication_date":"2023-02-03","ids":{"openalex":"https://openalex.org/W4319081346","doi":"https://doi.org/10.3390/sym15020414"},"language":"en","primary_location":{"id":"doi:10.3390/sym15020414","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020414","pdf_url":"https://www.mdpi.com/2073-8994/15/2/414/pdf?version=1675419579","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/2073-8994/15/2/414/pdf?version=1675419579","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067956384","display_name":"Markus Q. Huber","orcid":"https://orcid.org/0000-0002-7931-9801"},"institutions":[{"id":"https://openalex.org/I200763008","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","ror":"https://ror.org/033eqas34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200763008"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Markus Q. Huber","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik, Justus-Liebig-Universit\u00e4t Giessen, 35392 Giessen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik, Justus-Liebig-Universit\u00e4t Giessen, 35392 Giessen, Germany","institution_ids":["https://openalex.org/I200763008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039713393","display_name":"Wolfgang J. Kern","orcid":"https://orcid.org/0000-0001-5080-382X"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]},{"id":"https://openalex.org/I4210108044","display_name":"Nawi Graz","ror":"https://ror.org/01mm16571","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210108044"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Wolfgang J. Kern","raw_affiliation_strings":["Institute of Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstra\u00dfe 36, 8010 Graz, Austria","Institute of Physics, University of Graz, NAWI Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstra\u00dfe 36, 8010 Graz, Austria","institution_ids":["https://openalex.org/I4210108044","https://openalex.org/I15766117"]},{"raw_affiliation_string":"Institute of Physics, University of Graz, NAWI Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria","institution_ids":["https://openalex.org/I4210108044","https://openalex.org/I15766117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048904843","display_name":"Reinhard Alkofer","orcid":"https://orcid.org/0000-0001-7433-3295"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]},{"id":"https://openalex.org/I4210108044","display_name":"Nawi Graz","ror":"https://ror.org/01mm16571","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210108044"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Reinhard Alkofer","raw_affiliation_strings":["Institute of Physics, University of Graz, NAWI Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Physics, University of Graz, NAWI Graz, Universit\u00e4tsplatz 5, 8010 Graz, Austria","institution_ids":["https://openalex.org/I4210108044","https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067956384"],"corresponding_institution_ids":["https://openalex.org/I200763008"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.7773,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.87550039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"2","first_page":"414","last_page":"414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10527","display_name":"High-Energy Particle Collisions Research","score":0.9983999729156494,"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/quantum-chromodynamics","display_name":"Quantum chromodynamics","score":0.745056688785553},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6709275245666504},{"id":"https://openalex.org/keywords/gluon","display_name":"Gluon","score":0.49800586700439453},{"id":"https://openalex.org/keywords/quantum-field-theory","display_name":"Quantum field theory","score":0.47059452533721924},{"id":"https://openalex.org/keywords/correlation-function","display_name":"Correlation function (quantum field theory)","score":0.44754189252853394},{"id":"https://openalex.org/keywords/quark","display_name":"Quark","score":0.43856045603752136},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4384698271751404},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.42296403646469116},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.384602427482605},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.37234628200531006},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.32977378368377686},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32640182971954346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2694510221481323},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10991019010543823}],"concepts":[{"id":"https://openalex.org/C117137515","wikidata":"https://www.wikidata.org/wiki/Q238170","display_name":"Quantum chromodynamics","level":2,"score":0.745056688785553},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6709275245666504},{"id":"https://openalex.org/C123579102","wikidata":"https://www.wikidata.org/wiki/Q3299","display_name":"Gluon","level":3,"score":0.49800586700439453},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.47059452533721924},{"id":"https://openalex.org/C53622274","wikidata":"https://www.wikidata.org/wiki/Q2496679","display_name":"Correlation function (quantum field theory)","level":3,"score":0.44754189252853394},{"id":"https://openalex.org/C7602139","wikidata":"https://www.wikidata.org/wiki/Q6718","display_name":"Quark","level":2,"score":0.43856045603752136},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4384698271751404},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.42296403646469116},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.384602427482605},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.37234628200531006},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.32977378368377686},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32640182971954346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2694510221481323},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10991019010543823},{"id":"https://openalex.org/C133386390","wikidata":"https://www.wikidata.org/wiki/Q184996","display_name":"Dielectric","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15020414","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020414","pdf_url":"https://www.mdpi.com/2073-8994/15/2/414/pdf?version=1675419579","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:913610946edf4eaba4b2c9815f94e493","is_oa":true,"landing_page_url":"https://doaj.org/article/913610946edf4eaba4b2c9815f94e493","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 2, p 414 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/2/414/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15020414","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/sym15020414","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020414","pdf_url":"https://www.mdpi.com/2073-8994/15/2/414/pdf?version=1675419579","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":[],"awards":[{"id":"https://openalex.org/G1155167110","display_name":null,"funder_award_id":"FI 970/11-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4180104101","display_name":null,"funder_award_id":"05P21RGFP3","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G7225624288","display_name":null,"funder_award_id":"This work was","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G8330397625","display_name":null,"funder_award_id":"Funding","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4319081346.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1521687550","https://openalex.org/W1560287990","https://openalex.org/W1977645147","https://openalex.org/W1984825036","https://openalex.org/W1987818850","https://openalex.org/W1991662173","https://openalex.org/W1993858921","https://openalex.org/W1999582127","https://openalex.org/W2007377214","https://openalex.org/W2018159217","https://openalex.org/W2029449181","https://openalex.org/W2041885616","https://openalex.org/W2043267449","https://openalex.org/W2044585391","https://openalex.org/W2047702795","https://openalex.org/W2066953010","https://openalex.org/W2073508376","https://openalex.org/W2091776902","https://openalex.org/W2092617456","https://openalex.org/W2106653566","https://openalex.org/W2112244593","https://openalex.org/W2187004754","https://openalex.org/W2470904426","https://openalex.org/W2537927134","https://openalex.org/W2612911882","https://openalex.org/W2695371777","https://openalex.org/W2899104092","https://openalex.org/W2901512098","https://openalex.org/W2918404897","https://openalex.org/W2949156082","https://openalex.org/W2962205111","https://openalex.org/W3008791291","https://openalex.org/W3014443735","https://openalex.org/W3022614749","https://openalex.org/W3036797104","https://openalex.org/W3037023191","https://openalex.org/W3044839062","https://openalex.org/W3080752676","https://openalex.org/W3091923714","https://openalex.org/W3099225958","https://openalex.org/W3101155455","https://openalex.org/W3102651457","https://openalex.org/W3121183978","https://openalex.org/W3123019185","https://openalex.org/W3129599554","https://openalex.org/W3206963894","https://openalex.org/W4205788814","https://openalex.org/W4283752277","https://openalex.org/W4288060278","https://openalex.org/W4318562182","https://openalex.org/W4321094153","https://openalex.org/W6647068420"],"related_works":["https://openalex.org/W2029924341","https://openalex.org/W118170784","https://openalex.org/W179171457","https://openalex.org/W2059808423","https://openalex.org/W3099630975","https://openalex.org/W1988086507","https://openalex.org/W2037184473","https://openalex.org/W1978805690","https://openalex.org/W1564853914","https://openalex.org/W2045186166"],"abstract_inverted_index":{"The":[0,73],"analytic":[1,118],"structure":[2,119],"of":[3,7,16,18,32,44,56,102,120,124,130],"elementary":[4,121],"correlation":[5,33,122],"functions":[6,34,123],"a":[8,41,79,112],"quantum":[9,28,103,125],"field":[10],"is":[11,58,111],"relevant":[12],"for":[13,35,70,78,87,96,115],"the":[14,30,47,59,85,97,117,128],"calculation":[15,31,48,129],"masses":[17],"bound":[19],"states":[20],"and":[21,91,127],"their":[22],"time-like":[23,50],"properties":[24],"in":[25,107],"general.":[26],"In":[27],"chromodynamics,":[29],"purely":[36],"space-like":[37],"momenta":[38,51],"has":[39],"reached":[40],"high":[42],"level":[43],"sophistication,":[45],"but":[46,82],"at":[49],"requires":[52],"refined":[53],"methods.":[54],"One":[55],"them":[57],"contour":[60],"deformation":[61],"method.":[62],"Here":[63],"we":[64],"describe":[65],"how":[66],"to":[67],"employ":[68],"it":[69],"three-point":[71],"functions.":[72],"basic":[74],"mechanisms":[75],"are":[76,84,92],"discussed":[77],"scalar":[80],"theory,":[81],"they":[83],"same":[86],"more":[88],"complicated":[89],"theories":[90],"thus":[93],"relevant,":[94],"e.g.,":[95],"three-gluon":[98],"or":[99],"quark-gluon":[100],"vertices":[101],"chromodynamics.":[104],"Their":[105],"inclusion":[106],"existing":[108],"truncation":[109],"schemes":[110],"crucial":[113],"step":[114],"investigating":[116],"chromodynamics":[126],"its":[131],"spectrum":[132],"from":[133],"them.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
