{"id":"https://openalex.org/W1969449595","doi":"https://doi.org/10.1103/physrevd.10.3905","title":"Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization","display_name":"Conformal energy-momentum tensor in curved spacetime: Adiabatic regularization and renormalization","publication_year":1974,"publication_date":"1974-12-15","ids":{"openalex":"https://openalex.org/W1969449595","doi":"https://doi.org/10.1103/physrevd.10.3905","mag":"1969449595"},"language":"en","primary_location":{"id":"doi:10.1103/physrevd.10.3905","doi":"https://doi.org/10.1103/physrevd.10.3905","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevd.10.3905","pdf_url":null,"source":{"id":"https://openalex.org/S4210190737","display_name":"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields","issn_l":"0556-2821","issn":["0556-2821","1089-4918","1538-4500","1550-2368","1550-7998"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review D","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/A5001976934","display_name":"S. A. Fulling","orcid":"https://orcid.org/0000-0003-2309-5965","observed_orcids":["https://orcid.org/0000-0003-2309-5965"]},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. A. Fulling","raw_affiliation_strings":["Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102566634","display_name":"Leonard Parker","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leonard Parker","raw_affiliation_strings":["Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056163037","display_name":"B. L. Hu","orcid":"https://orcid.org/0000-0003-2489-9914","observed_orcids":["https://orcid.org/0000-0003-2489-9914"]},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. L. Hu","raw_affiliation_strings":["Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201","Physics Department Stanford University Stanford, California 94305"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201","institution_ids":["https://openalex.org/I43579087"]},{"raw_affiliation_string":"Physics Department Stanford University Stanford, California 94305","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.2321,"has_fulltext":false,"cited_by_count":297,"citation_normalized_percentile":{"value":0.98215452,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"10","issue":"12","first_page":"3905","last_page":"3924"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9585000276565552,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9585000276565552,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.02199999988079071,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.009399999864399433,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conformal-coupling","display_name":"conformal coupling","score":0.8690000176429749},{"id":"https://openalex.org/keywords/energy-momentum-tensor","display_name":"energy-momentum tensor","score":0.9049999713897705},{"id":"https://openalex.org/keywords/adiabatic-regularization","display_name":"adiabatic regularization","score":0.8399999737739563},{"id":"https://openalex.org/keywords/renormalization","display_name":"renormalization","score":0.984000027179718},{"id":"https://openalex.org/keywords/quantum-scalar-field","display_name":"quantum scalar field","score":0.6309999823570251},{"id":"https://openalex.org/keywords/kasner-metric","display_name":"Kasner metric","score":0.6570000052452087},{"id":"https://openalex.org/keywords/robertson-walker-metric","display_name":"Robertson-Walker metric","score":0.8600000143051147},{"id":"https://openalex.org/keywords/anisotropic-cosmological-models","display_name":"anisotropic cosmology","score":0.7490000128746033},{"id":"https://openalex.org/keywords/cosmological-constant","display_name":"cosmological constant","score":0.7179999947547913},{"id":"https://openalex.org/keywords/vacuum-energy","display_name":"vacuum energy","score":0.6729999780654907},{"id":"https://openalex.org/keywords/conformal-flatness","display_name":"conformal flatness","score":0.7739999890327454}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8055615425109863},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5396963953971863},{"id":"https://openalex.org/C120484201","wikidata":"https://www.wikidata.org/wiki/Q2246697","display_name":"Quantum field theory in curved spacetime","level":4,"score":0.5295266509056091},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.5191166400909424},{"id":"https://openalex.org/C191696108","wikidata":"https://www.wikidata.org/wiki/Q876346","display_name":"Stress\u2013energy tensor","level":3,"score":0.48273012042045593},{"id":"https://openalex.org/C14440778","wikidata":"https://www.wikidata.org/wiki/Q550929","display_name":"Einstein tensor","level":4,"score":0.45878344774246216},{"id":"https://openalex.org/C8466233","wikidata":"https://www.wikidata.org/wiki/Q757269","display_name":"Metric tensor","level":3,"score":0.4533322751522064},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.44597744941711426},{"id":"https://openalex.org/C166124518","wikidata":"https://www.wikidata.org/wiki/Q1047702","display_name":"Renormalization","level":2,"score":0.4289165437221527},{"id":"https://openalex.org/C6947382","wikidata":"https://www.wikidata.org/wiki/Q1143773","display_name":"Vacuum energy","level":2,"score":0.425203800201416},{"id":"https://openalex.org/C166861157","wikidata":"https://www.wikidata.org/wiki/Q59151","display_name":"Cosmological constant","level":2,"score":0.42107588052749634},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3092108964920044},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2871544361114502},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.2604844272136688},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.24629977345466614},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.12829264998435974},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11634546518325806},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.0852571427822113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrevd.10.3905","doi":"https://doi.org/10.1103/physrevd.10.3905","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevd.10.3905","pdf_url":null,"source":{"id":"https://openalex.org/S4210190737","display_name":"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields","issn_l":"0556-2821","issn":["0556-2821","1089-4918","1538-4500","1550-2368","1550-7998"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review D","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":17,"referenced_works":["https://openalex.org/W1966716804","https://openalex.org/W1967340946","https://openalex.org/W1973624731","https://openalex.org/W1974281514","https://openalex.org/W1981729129","https://openalex.org/W1994049919","https://openalex.org/W2030245340","https://openalex.org/W2055055246","https://openalex.org/W2063894837","https://openalex.org/W2079890182","https://openalex.org/W2127601777","https://openalex.org/W2132698299","https://openalex.org/W2149169547","https://openalex.org/W2318111158","https://openalex.org/W3140714191","https://openalex.org/W4230959423","https://openalex.org/W4238731570"],"related_works":["https://openalex.org/W1981729129","https://openalex.org/W1973624731","https://openalex.org/W2109407967","https://openalex.org/W2013411491","https://openalex.org/W2062622323","https://openalex.org/W2019919163","https://openalex.org/W188891829","https://openalex.org/W1987594554","https://openalex.org/W2037233848","https://openalex.org/W1977414656"],"abstract_inverted_index":{"In":[0,113,173],"preparation":[1],"for":[2,103],"an":[3,96],"investigation":[4],"of":[5,30,79,99,107,120,159,178,203,211,228,235],"whether":[6],"field-theoretic":[7],"effects":[8],"helped":[9],"to":[10,19,44,131,134,243,251],"make":[11],"the":[12,21,28,45,52,65,77,100,104,108,114,121,125,136,147,160,174,186,194,204,212,226,255],"early":[13],"universe":[14],"become":[15],"isotropic,":[16],"we":[17],"seek":[18],"determine":[20],"physical":[22],"(divergence-free)":[23],"energy-momentum":[24,154],"tensor":[25,138,143,155],"through":[26],"which":[27,144,222,240],"geometry":[29],"spacetime":[31,148,224],"is":[32,149,182,196,207,214,241,249],"influenced":[33],"by":[34,216],"a":[35,80,86,117,140,152,169,200,218,229],"quantized":[36],"scalar":[37,83],"field":[38,84],"with":[39,254],"conformal":[40,179],"(\"new":[41],"improved\")":[42],"coupling":[43,166],"metric.":[46,88],"The":[47,69,209,232],"cosmological":[48,161],"models":[49],"studied":[50],"are":[51,93],"Kasner-like":[53],"(type":[54],"I)":[55],"metrics":[56],"(homogeneous,":[57],"spatially":[58],"flat,":[59],"nonrotating,":[60],"but":[61],"anisotropic),":[62],"and":[63,85,111,163,238,246],"also":[64],"isotropic":[66],"Robertson-Walker":[67,87,175],"metrics.":[68],"methods":[70,213],"employed":[71],"have":[72],"previously":[73],"been":[74],"expounded":[75],"in":[76,124,168,221],"context":[78],"minimally":[81],"coupled":[82],"Three":[89],"divergent":[90,189],"leading":[91,122],"terms":[92,123],"extracted":[94],"from":[95],"adiabatic":[97,233],"expansion":[98,245],"formal":[101],"expressions":[102],"expectation":[105],"values":[106],"energy":[109,126],"density":[110,127],"pressures.":[112],"Kasner":[115,230],"case":[116],"slight":[118],"reshuffling":[119],"displays":[128],"all":[129],"divergences":[130],"be":[132,252],"proportional":[133],"either":[135],"metric":[137],"or":[139],"second-order":[141],"curvature":[142],"vanishes":[145],"when":[146,193],"isotropic;":[150],"hence":[151],"finite":[153,201],"remains":[156],"after":[157],"renormalization":[158,202,247],"constant":[162,167,190,206],"one":[164],"other":[165],"generalized":[170],"Einstein":[171],"equation.":[172],"cases,":[176],"because":[177],"flatness,":[180],"there":[181],"no":[183],"divergence":[184],"beyond":[185],"usual":[187,256],"quartically":[188],"vacuum":[191],"energy;":[192],"mass":[195],"not":[197],"zero,":[198],"however,":[199],"gravitational":[205],"suggested.":[208],"correctness":[210],"tested":[215],"considering":[217],"coordinate":[219],"system":[220],"flat":[223],"assumes":[225],"form":[227],"universe:":[231],"definition":[234],"particle":[236],"number":[237],"vacuum,":[239],"basic":[242],"our":[244],"methods,":[248],"seen":[250],"consistent":[253],"flat-space":[257],"concepts.":[258]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":35},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
