{"id":"https://openalex.org/W7225615532","doi":"https://doi.org/10.5281/zenodo.24068353","title":"The Scretching\u2013Planck Action as a Path Integral: Density and Phase from the Sum over Histories","display_name":"The Scretching\u2013Planck Action as a Path Integral: Density and Phase from the Sum over Histories","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225615532","doi":"https://doi.org/10.5281/zenodo.24068353"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24068353","doi":"https://doi.org/10.5281/zenodo.24068353","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068353","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24068353","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134268878","display_name":"Daniel Scretching","orcid":"https://orcid.org/0009-0008-9586-2717","observed_orcids":["https://orcid.org/0009-0008-9586-2717"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Scretching, Daniel","raw_affiliation_strings":["Scretching Quantum Press LLC"],"raw_orcid":"https://orcid.org/0009-0008-9586-2717","affiliations":[{"raw_affiliation_string":"Scretching Quantum Press LLC","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5134268878"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.8823000192642212,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.8823000192642212,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.03620000183582306,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.014999999664723873,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/quantum-potential","display_name":"quantum potential","score":0.7979999780654907},{"id":"https://openalex.org/keywords/hamilton-jacobi-equation","display_name":"Hamilton-Jacobi equation","score":0.8320000171661377},{"id":"https://openalex.org/keywords/stationary-phase","display_name":"stationary phase","score":0.5699999928474426},{"id":"https://openalex.org/keywords/transfer-matrix","display_name":"transfer matrix","score":0.546999990940094},{"id":"https://openalex.org/keywords/ground-state-energy","display_name":"ground state energy","score":0.8029999732971191},{"id":"https://openalex.org/keywords/double-well","display_name":"double well","score":0.6290000081062317},{"id":"https://openalex.org/keywords/path-integral-monte-carlo","display_name":"path integral Monte Carlo","score":0.8389999866485596},{"id":"https://openalex.org/keywords/diffusion","display_name":"diffusion","score":0.32600000500679016},{"id":"https://openalex.org/keywords/aharonov-bohm-phase","display_name":"Aharonov-Bohm phase","score":0.8629999756813049},{"id":"https://openalex.org/keywords/magnetic-flux","display_name":"magnetic flux","score":0.5630000233650208},{"id":"https://openalex.org/keywords/imaginary-time","display_name":"imaginary time","score":0.49000000953674316}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6409000158309937},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.515999972820282},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C154018700","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Path integral formulation","level":3,"score":0.5073000192642212},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4715999960899353},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.4465999901294708},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4203999936580658},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.41929998993873596},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37299999594688416},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.34049999713897705},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.30219998955726624},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.2782000005245209},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.26600000262260437},{"id":"https://openalex.org/C52704855","wikidata":"https://www.wikidata.org/wiki/Q1126603","display_name":"Elliptic integral","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.25220000743865967},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.25209999084472656},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24068353","doi":"https://doi.org/10.5281/zenodo.24068353","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068353","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24068354","doi":"https://doi.org/10.5281/zenodo.24068354","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068354","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24068353","doi":"https://doi.org/10.5281/zenodo.24068353","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068353","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225309048","https://openalex.org/W7225073257","https://openalex.org/W2034008385","https://openalex.org/W1751445117","https://openalex.org/W3009735314","https://openalex.org/W39751989","https://openalex.org/W7096715598","https://openalex.org/W7100772789","https://openalex.org/W2046169189","https://openalex.org/W7225295185"],"abstract_inverted_index":{"This":[0],"paper":[1],"formulates":[2],"the":[3,16,24,34,44,55,58,69,72,77,94,102,106,115,120,124,134,142,151,174,179,189],"Schr\u00f6dinger":[4,17],"field":[5],"path":[6],"integral":[7],"in":[8,28,119,165,188],"Scretching\u2013Planck":[9],"(SP)":[10],"density\u2013phase":[11],"variables,":[12],"\\(\\psi=\\sqrt{P}\\,e^{iS/\\hbar}\\).":[13],"Substituting":[14],"into":[15,145],"Lagrangian":[18],"gives":[19,130],"\\(\\mathcal":[20],"L_{\\mathrm{Sch}}=-\\mathcal":[21],"L_{\\mathrm{SP}}\\),":[22],"so":[23],"real-time":[25],"action":[26],"weight":[27],"these":[29],"variables":[30],"is":[31,52,64,97,150],"\\(e^{-iS_{\\mathrm{SP}}/\\hbar}\\).":[32],"In":[33,68,99],"particle":[35],"propagator,":[36],"stationary":[37,116,158],"phase":[38],"recovers":[39],"Hamilton\u2019s":[40],"principal":[41],"function":[42],"and":[43,66,109,178],"Van":[45],"Vleck":[46],"amplitude.":[47],"The":[48,80,111,156],"SP":[49,81,175],"quantum":[50,95],"potential":[51],"determined":[53],"by":[54,163,171],"curvature":[56],"of":[57,88],"propagator\u2019s":[59],"amplitude":[60,63],"wherever":[61],"that":[62],"regular":[65],"nonzero.":[67],"time-sliced":[70],"example,":[71],"error":[73],"decreases":[74],"quadratically":[75],"with":[76,91,133,182],"time":[78],"step.":[79],"Hamilton\u2013Jacobi":[82],"equation":[83],"has":[84],"an":[85],"RMS":[86],"residual":[87],"\\(1.6\\times10^{-4}\\),":[89],"compared":[90,132],"\\(1.365\\)":[92],"when":[93],"term":[96],"omitted.":[98],"imaginary":[100],"time,":[101],"transfer":[103],"matrix":[104],"extracts":[105],"ground-state":[107,139],"energy":[108],"density.":[110],"resulting":[112],"density":[113,159],"satisfies":[114],"balance":[117],"\\(V+Q_{\\mathrm{SP}}[P_0]=E_0\\)":[118],"benchmark":[121],"calculations.":[122],"For":[123,167],"double":[125],"well,":[126],"path-integral":[127],"Monte":[128],"Carlo":[129],"\\(E_0=1.1458\\pm0.0023\\),":[131],"reference":[135],"value":[136],"\\(1.1439\\).":[137],"A":[138],"transformation":[140],"converts":[141],"Euclidean":[143],"evolution":[144],"a":[146,168],"diffusion":[147],"whose":[148],"drift":[149],"osmotic":[152],"velocity":[153],"\\(u=(\\hbar/2m)\\partial_x\\ln":[154],"P_0\\).":[155],"simulated":[157],"differs":[160],"from":[161],"\\(P_0\\)":[162],"\\(0.0033\\)":[164],"\\(L^1\\).":[166],"ring":[169],"threaded":[170],"magnetic":[172],"flux,":[173],"circulation":[176],"sum":[177,181],"path-winding":[180],"Aharonov\u2013Bohm":[183],"phases":[184],"agree":[185],"to":[186],"\\(2.5\\times10^{-16}\\)":[187],"numerical":[190],"check.":[191],"Eight":[192],"solved":[193],"problems":[194],"are":[195],"included.":[196]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}