1986-04
AUTHORSCécile DeWitt-Morette, Stephen G. Low, Lawrence S. Schulman, Anwar Y. Shiekh
ABSTRACTThe wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results—hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value problem of differential equations; solutions defined on mutiply connected spaces. Section 3: geometrical theory of diffraction; identificiation of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a μ-sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function. More... »
PAGES311-349
http://scigraph.springernature.com/pub.10.1007/bf01882691
DOIhttp://dx.doi.org/10.1007/bf01882691
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1033936239
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT
[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
"about": [
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "The University of Texas at Austin",
"id": "https://www.grid.ac/institutes/grid.89336.37",
"name": [
"Department of Physics and Center for Relativity, University of Texas, 78712, Austin, Texas"
],
"type": "Organization"
},
"familyName": "DeWitt-Morette",
"givenName": "C\u00e9cile",
"id": "sg:person.011647320362.04",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011647320362.04"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "The University of Texas at Austin",
"id": "https://www.grid.ac/institutes/grid.89336.37",
"name": [
"Department of Physics and Center for Relativity, University of Texas, 78712, Austin, Texas"
],
"type": "Organization"
},
"familyName": "Low",
"givenName": "Stephen G.",
"id": "sg:person.015101622232.18",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015101622232.18"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Clarkson University",
"id": "https://www.grid.ac/institutes/grid.254280.9",
"name": [
"Department of Physics, Technion, Haifa, Israel",
"Department of Physics, Clarkson University, 13676, Potsdam, New York"
],
"type": "Organization"
},
"familyName": "Schulman",
"givenName": "Lawrence S.",
"id": "sg:person.010275521604.97",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010275521604.97"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Imperial College London",
"id": "https://www.grid.ac/institutes/grid.7445.2",
"name": [
"Blackett Laboratory, Imperial College, SW7 2BZ, London"
],
"type": "Organization"
},
"familyName": "Shiekh",
"givenName": "Anwar Y.",
"id": "sg:person.013541627022.35",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013541627022.35"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/bf02099371",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1000430937",
"https://doi.org/10.1007/bf02099371"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02099371",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1000430937",
"https://doi.org/10.1007/bf02099371"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/3540070729_27",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009254752",
"https://doi.org/10.1007/3540070729_27"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/3-540-07553-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009878312",
"https://doi.org/10.1007/3-540-07553-4"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/3-540-07553-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009878312",
"https://doi.org/10.1007/3-540-07553-4"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0378-4371(83)90096-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1013328119"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0378-4371(83)90096-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1013328119"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/sapm192433127",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019681407"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0003-4916(59)90027-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1022577597"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0003-4916(86)90141-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1022779135"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160200205",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1023781511"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160200205",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1023781511"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01646034",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024834671",
"https://doi.org/10.1007/bf01646034"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01646034",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024834671",
"https://doi.org/10.1007/bf01646034"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-7091-8780-7_5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024883126",
"https://doi.org/10.1007/978-3-7091-8780-7_5"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0370-1573(79)90083-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1028787920"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0370-1573(79)90083-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1028787920"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0034-4885/35/1/306",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1029551806"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-7091-8780-7_6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1030903509",
"https://doi.org/10.1007/978-3-7091-8780-7_6"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0378-4371(83)90097-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032211210"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0378-4371(83)90097-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032211210"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0003-4916(76)90041-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1041159012"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0003-4916(59)90026-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1042925040"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.115.485",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043456385"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.115.485",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043456385"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/3540075534_6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043859196",
"https://doi.org/10.1007/3540075534_6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01447273",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044358319",
"https://doi.org/10.1007/bf01447273"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0003-4916(76)90040-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044375868"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0003-4916(86)90060-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1047573737"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1063/1.1664835",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1057742890"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1063/1.1665592",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1057743672"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1063/1.523843",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1058100863"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1070/rm1975v030n01abeh001400",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1058194149"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0143-0807/1/3/008",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059034281"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0143-0807/1/4/011",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059034298"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0143-0807/5/1/011",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059037533"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0305-4470/16/13/023",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059066455"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0305-4470/16/3/011",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059066682"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1088/0370-1328/91/3/301",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1059096144"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.176.1558",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060440042"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.176.1558",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060440042"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.54.924",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060450266"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.54.924",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060450266"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.54.931",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060450268"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.54.931",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060450268"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.81.848",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060457491"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrev.81.848",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060457491"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevd.29.1663",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060691140"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevd.29.1663",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060691140"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevd.3.1375",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060691517"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevd.3.1375",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060691517"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevlett.49.599",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060787992"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/physrevlett.49.599",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060787992"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/revmodphys.57.339",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060839068"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1103/revmodphys.57.339",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1060839068"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1112/plms/s1-30.1.121",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062057076"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1119/1.12720",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062229813"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1364/josa.52.000116",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1065148071"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4684-7592-0_5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1089762899",
"https://doi.org/10.1007/978-1-4684-7592-0_5"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1080/00029890.1975.11993855",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1103212389"
],
"type": "CreativeWork"
}
],
"datePublished": "1986-04",
"datePublishedReg": "1986-04-01",
"description": "The wedge problem, that is, the propagation of radiation or particles in the presence of a wedge, is examined in different contexts. Generally, the paper follows the historical order from Sommerfeld's early work to recent stochastic results\u2014hindsights and new results being woven in as appropriate. In each context, identifying the relevant mathematical problem has been the key to the solution. Thus each section can be given both a physics and a mathematics title: Section 2: diffraction by reflecting wedge; boundary value problem of differential equations; solutions defined on mutiply connected spaces. Section 3: geometrical theory of diffraction; identificiation of function spaces. Section 4: path integral solutions; path integration on multiply connected spaces; asymptotics on the boundaries of function spaces. Section 5: probing the shape of the wedge and the roughness of its surface; stochastic calculus. Several propagators and Green functions are given explicitly, some old ones and some new ones. They include the knife-edge propagator for Dirichlet and Neumann boundary conditions, the absorbing knife edge propagator, the wedge propagators, the propagator for a free particle on a \u03bc-sheeted Riemann surface, the Dirichlet and the Neumann wedge Green function.",
"genre": "research_article",
"id": "sg:pub.10.1007/bf01882691",
"inLanguage": [
"en"
],
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1297335",
"issn": [
"0015-9018",
"1572-9516"
],
"name": "Foundations of Physics",
"type": "Periodical"
},
{
"issueNumber": "4",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "16"
}
],
"name": "Wedges I",
"pagination": "311-349",
"productId": [
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"a1a9ce25279c3b1ffd8d67a2eb2876b0c3f0d65d919fe668bbec8c21fe549a35"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/bf01882691"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1033936239"
]
}
],
"sameAs": [
"https://doi.org/10.1007/bf01882691",
"https://app.dimensions.ai/details/publication/pub.1033936239"
],
"sdDataset": "articles",
"sdDatePublished": "2019-04-11T10:52",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000351_0000000351/records_43226_00000000.jsonl",
"type": "ScholarlyArticle",
"url": "http://link.springer.com/10.1007/BF01882691"
}
]Download the RDF metadata as: json-ld nt turtle xml License info
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf01882691'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf01882691'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01882691'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01882691'
This table displays all metadata directly associated to this object as RDF triples.
230 TRIPLES
21 PREDICATES
71 URIs
19 LITERALS
7 BLANK NODES