{"id":"https://openalex.org/W3187483511","doi":"https://doi.org/10.22331/q-2022-04-21-694","title":"Time-Slicing Path-integral in Curved Space","display_name":"Time-Slicing Path-integral in Curved Space","publication_year":2022,"publication_date":"2022-04-21","ids":{"openalex":"https://openalex.org/W3187483511","doi":"https://doi.org/10.22331/q-2022-04-21-694","mag":"3187483511"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-04-21-694","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-21-694","pdf_url":"https://quantum-journal.org/papers/q-2022-04-21-694/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2022-04-21-694/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066415657","display_name":"Mingnan Ding","orcid":"https://orcid.org/0000-0002-2205-5809"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingnan Ding","raw_affiliation_strings":["Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032532531","display_name":"Xiangjun Xing","orcid":"https://orcid.org/0000-0003-0822-0588"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangjun Xing","raw_affiliation_strings":["Shanghai Research Center for Quantum Sciences, Shanghai 201315 China","T.D. Lee Institute, Shanghai Jiao Tong University, Shanghai, 200240 China","Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Research Center for Quantum Sciences, Shanghai 201315 China","institution_ids":[]},{"raw_affiliation_string":"T.D. Lee Institute, Shanghai Jiao Tong University, Shanghai, 200240 China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.8765,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.70935682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"6","issue":null,"first_page":"694","last_page":"694"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9952999949455261,"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/algorithm","display_name":"Algorithm","score":0.45410239696502686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3934314548969269}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45410239696502686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3934314548969269}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2022-04-21-694","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-21-694","pdf_url":"https://quantum-journal.org/papers/q-2022-04-21-694/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2107.14562","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2107.14562","pdf_url":"https://arxiv.org/pdf/2107.14562","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:9fc3e4ebcf7d4e148c557a04fed63922","is_oa":true,"landing_page_url":"https://doaj.org/article/9fc3e4ebcf7d4e148c557a04fed63922","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":"Quantum, Vol 6, p 694 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-04-21-694","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-21-694","pdf_url":"https://quantum-journal.org/papers/q-2022-04-21-694/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5311504058","display_name":"\u7535\u89e3\u6db2\u754c\u9762\u7cfb\u7edf\u7684\u7edf\u8ba1\u7269\u7406\u7814\u7a76","funder_award_id":"11674217","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3187483511.pdf","grobid_xml":"https://content.openalex.org/works/W3187483511.grobid-xml"},"referenced_works_count":93,"referenced_works":["https://openalex.org/W225968618","https://openalex.org/W569564947","https://openalex.org/W1483893079","https://openalex.org/W1484033701","https://openalex.org/W1540131366","https://openalex.org/W1544741952","https://openalex.org/W1552242395","https://openalex.org/W1552736770","https://openalex.org/W1562682436","https://openalex.org/W1600201693","https://openalex.org/W1604189802","https://openalex.org/W1618867321","https://openalex.org/W1651652924","https://openalex.org/W1653368542","https://openalex.org/W1663426805","https://openalex.org/W1676019512","https://openalex.org/W1850008116","https://openalex.org/W1964417700","https://openalex.org/W1964706495","https://openalex.org/W1965075382","https://openalex.org/W1977644564","https://openalex.org/W1987866832","https://openalex.org/W1989659612","https://openalex.org/W1991508523","https://openalex.org/W1992028409","https://openalex.org/W1997093580","https://openalex.org/W2001013411","https://openalex.org/W2006233704","https://openalex.org/W2010463447","https://openalex.org/W2011136538","https://openalex.org/W2012321369","https://openalex.org/W2025830947","https://openalex.org/W2026532628","https://openalex.org/W2030901711","https://openalex.org/W2031320386","https://openalex.org/W2032251395","https://openalex.org/W2034820138","https://openalex.org/W2036573615","https://openalex.org/W2045496721","https://openalex.org/W2051594385","https://openalex.org/W2056666535","https://openalex.org/W2057189552","https://openalex.org/W2057195948","https://openalex.org/W2060652909","https://openalex.org/W2061702035","https://openalex.org/W2063667346","https://openalex.org/W2068657229","https://openalex.org/W2077195753","https://openalex.org/W2077626691","https://openalex.org/W2078634751","https://openalex.org/W2083200102","https://openalex.org/W2084373176","https://openalex.org/W2086360439","https://openalex.org/W2086897729","https://openalex.org/W2097246107","https://openalex.org/W2102787760","https://openalex.org/W2110023503","https://openalex.org/W2114464239","https://openalex.org/W2150439050","https://openalex.org/W2197645166","https://openalex.org/W2328151902","https://openalex.org/W2491953512","https://openalex.org/W2496901226","https://openalex.org/W2591313944","https://openalex.org/W2607432770","https://openalex.org/W2733029667","https://openalex.org/W2968509759","https://openalex.org/W3022585649","https://openalex.org/W3045864679","https://openalex.org/W3046221631","https://openalex.org/W3098465643","https://openalex.org/W3102788270","https://openalex.org/W3103795148","https://openalex.org/W3104388276","https://openalex.org/W3104808187","https://openalex.org/W3105457728","https://openalex.org/W3122810280","https://openalex.org/W3197980391","https://openalex.org/W4212834654","https://openalex.org/W4230384102","https://openalex.org/W4230895289","https://openalex.org/W4230934093","https://openalex.org/W4235028801","https://openalex.org/W4241053470","https://openalex.org/W4301003629","https://openalex.org/W4302050383","https://openalex.org/W4302423216","https://openalex.org/W6625156598","https://openalex.org/W6633243065","https://openalex.org/W6635956400","https://openalex.org/W6637506333","https://openalex.org/W6753059429","https://openalex.org/W6803200229"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Path":[0],"integrals":[1,59],"constitute":[2],"powerful":[3],"representations":[4,94],"for":[5,27,60,71,95,103],"both":[6],"quantum":[7],"and":[8,53,185],"stochastic":[9],"dynamics.":[10],"Yet":[11],"despite":[12],"many":[13,92],"decades":[14],"of":[15,43,56,90,126,161,175],"intensive":[16],"studies,":[17],"there":[18],"is":[19,178,183],"no":[20],"consensus":[21],"on":[22],"how":[23,33,167],"to":[24,34,40,115],"formulate":[25],"them":[26,36],"dynamics":[28,61,105],"in":[29,62,80],"curved":[30,63],"space,":[31],"or":[32],"make":[35],"covariant":[37,54],"with":[38,106],"respect":[39],"nonlinear":[41],"transform":[42],"variables":[44],"(NTV).":[45],"In":[46],"this":[47],"work,":[48],"we":[49,156],"construct":[50,122],"a":[51,68,116,123,188],"rigorous":[52,69],"formulation":[55],"time-slicing":[57,96],"path":[58,97],"space.":[64],"We":[65,99,120],"first":[66],"establish":[67,158],"criterion":[70],"equivalence":[72],"of<mml:math":[73],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[74,198],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[75,199],"class=\"MJX-tex-mathit\"":[76,200],"mathvariant=\"italic\">time-slice":[77],"Green's":[78],"function</mml:mtext></mml:mrow></mml:math>(TSGF)":[79],"the":[81,88,159,168],"continuum":[82],"limit":[83],"(Lemma":[84,118],"1).":[85],"This":[86],"implies":[87],"existence":[89],"infinitely":[91],"equivalent":[93,114,127],"integral.":[98],"then":[100],"show":[101],"that,":[102],"any":[104],"second":[107],"order":[108],"generator,":[109],"all":[110],"time-slice":[111,176],"actions":[112,129],"are":[113],"Gaussian":[117,184],"2).":[119],"further":[121],"continuous":[124],"family":[125],"path-integral":[128,163],"parameterized":[130],"by":[131,165],"an":[132],"interpolation":[133],"parameter<mml:math":[134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>&amp;#x03B1;</mml:mi><mml:mo>&amp;#x2208;</mml:mo><mml:mo":[135],"stretchy=\"false\">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo":[136],"stretchy=\"false\">]</mml:mo></mml:math>(Lemma":[137],"3).":[138],"The":[139],"action":[140,169,177],"generically":[141],"contains":[142],"term":[143],"linear":[144],"in<mml:math":[145],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi":[146,193],"mathvariant=\"normal\">&amp;#x0394;</mml:mi><mml:mi":[147,194],"mathvariant=\"bold-italic\">x</mml:mi></mml:math>,":[148],"whose":[149],"concrete":[150],"form":[151],"depends":[152],"on<mml:math":[153],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>&amp;#x03B1;</mml:mi></mml:math>.":[154],"Finally":[155],"also":[157],"covariance":[160],"our":[162],"formalism,":[164],"demonstrating":[166],"transforms":[170,186],"under":[171],"NTV.":[172],"The<mml:math":[173],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>&amp;#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>representation":[174],"particularly":[179],"convenient":[180],"because":[181],"it":[182],"as":[187,190],"scalar,":[189],"long":[191],"as<mml:math":[192],"mathvariant=\"bold-italic\">x</mml:mi></mml:math>transforms":[195],"according":[196],"to<mml:math":[197],"mathvariant=\"italic\">Ito's":[201],"formula</mml:mtext></mml:mrow></mml:math>.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
