Proof of the Bogoliubov-Parasiuk theorem on renormalization View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1966-12

AUTHORS

Klaus Hepp

ABSTRACT

A new proof is given that the subtraction rules ofBogoliubov andParasiuk lead to well-defined renormalized Green's distributions. A collection of the counter-terms in “trees” removes the difficulties with overlapping divergences and allows fairly simple estimates and closed expressions for renormalized Feynman integrals. The renormalization procedure, which also applies to conventionally non-renormalizable theories, is illustrated in the ϕ4-theory. More... »

PAGES

301-326

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01773358

DOI

http://dx.doi.org/10.1007/bf01773358

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1025559985


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

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/2008/1701", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Psychology", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/17", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Psychology and Cognitive Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institute for Advanced Study", 
          "id": "https://www.grid.ac/institutes/grid.78989.37", 
          "name": [
            "The Institute for Advanced Study, Princeton, New Jersey"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hepp", 
        "givenName": "Klaus", 
        "id": "sg:person.015150461215.30", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015150461215.30"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02392399", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042147174", 
          "https://doi.org/10.1007/bf02392399"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.21.434", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042535342"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.21.434", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042535342"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02526406", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054502463", 
          "https://doi.org/10.1007/bf02526406"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.125.1436", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060424916"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.125.1436", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060424916"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.75.486", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060454988"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.75.486", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060454988"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.80.268", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060456916"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.80.268", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060456916"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.82.217", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060457594"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.82.217", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060457594"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1966-12", 
    "datePublishedReg": "1966-12-01", 
    "description": "A new proof is given that the subtraction rules ofBogoliubov andParasiuk lead to well-defined renormalized Green's distributions. A collection of the counter-terms in \u201ctrees\u201d removes the difficulties with overlapping divergences and allows fairly simple estimates and closed expressions for renormalized Feynman integrals. The renormalization procedure, which also applies to conventionally non-renormalizable theories, is illustrated in the \u03d54-theory.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf01773358", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136216", 
        "issn": [
          "0010-3616", 
          "1432-0916"
        ], 
        "name": "Communications in Mathematical Physics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2"
      }
    ], 
    "name": "Proof of the Bogoliubov-Parasiuk theorem on renormalization", 
    "pagination": "301-326", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "79c4df76dfd1f3827a631ee18764d4f12034e60965dd5b1d8064757c3aef9d29"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf01773358"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1025559985"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf01773358", 
      "https://app.dimensions.ai/details/publication/pub.1025559985"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T09:57", 
    "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/v90/0000000347_0000000347/records_89807_00000001.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF01773358"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

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/bf01773358'

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/bf01773358'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01773358'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01773358'


 

This table displays all metadata directly associated to this object as RDF triples.

84 TRIPLES      21 PREDICATES      34 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf01773358 schema:about anzsrc-for:17
2 anzsrc-for:1701
3 schema:author Naf87bae01dca4efea8cedbf02b43cb38
4 schema:citation sg:pub.10.1007/bf02392399
5 sg:pub.10.1007/bf02526406
6 https://doi.org/10.1103/physrev.125.1436
7 https://doi.org/10.1103/physrev.75.486
8 https://doi.org/10.1103/physrev.80.268
9 https://doi.org/10.1103/physrev.82.217
10 https://doi.org/10.1103/revmodphys.21.434
11 schema:datePublished 1966-12
12 schema:datePublishedReg 1966-12-01
13 schema:description A new proof is given that the subtraction rules ofBogoliubov andParasiuk lead to well-defined renormalized Green's distributions. A collection of the counter-terms in “trees” removes the difficulties with overlapping divergences and allows fairly simple estimates and closed expressions for renormalized Feynman integrals. The renormalization procedure, which also applies to conventionally non-renormalizable theories, is illustrated in the ϕ4-theory.
14 schema:genre research_article
15 schema:inLanguage en
16 schema:isAccessibleForFree false
17 schema:isPartOf N7c3f9e487af2442b8a893f845c0952e4
18 Nb377eba1e18142eb9680f9ab9a34205f
19 sg:journal.1136216
20 schema:name Proof of the Bogoliubov-Parasiuk theorem on renormalization
21 schema:pagination 301-326
22 schema:productId N267478249c314e6fb5ac389ffbd1efaa
23 N6b43bece8e8b41f9bc8586c5162bdf19
24 N9c5b42c92fc74b7e859e6d23a7a21a23
25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025559985
26 https://doi.org/10.1007/bf01773358
27 schema:sdDatePublished 2019-04-11T09:57
28 schema:sdLicense https://scigraph.springernature.com/explorer/license/
29 schema:sdPublisher N297fca7f3442477f83d2321897a4e8c0
30 schema:url http://link.springer.com/10.1007/BF01773358
31 sgo:license sg:explorer/license/
32 sgo:sdDataset articles
33 rdf:type schema:ScholarlyArticle
34 N267478249c314e6fb5ac389ffbd1efaa schema:name dimensions_id
35 schema:value pub.1025559985
36 rdf:type schema:PropertyValue
37 N297fca7f3442477f83d2321897a4e8c0 schema:name Springer Nature - SN SciGraph project
38 rdf:type schema:Organization
39 N6b43bece8e8b41f9bc8586c5162bdf19 schema:name doi
40 schema:value 10.1007/bf01773358
41 rdf:type schema:PropertyValue
42 N7c3f9e487af2442b8a893f845c0952e4 schema:volumeNumber 2
43 rdf:type schema:PublicationVolume
44 N9c5b42c92fc74b7e859e6d23a7a21a23 schema:name readcube_id
45 schema:value 79c4df76dfd1f3827a631ee18764d4f12034e60965dd5b1d8064757c3aef9d29
46 rdf:type schema:PropertyValue
47 Naf87bae01dca4efea8cedbf02b43cb38 rdf:first sg:person.015150461215.30
48 rdf:rest rdf:nil
49 Nb377eba1e18142eb9680f9ab9a34205f schema:issueNumber 1
50 rdf:type schema:PublicationIssue
51 anzsrc-for:17 schema:inDefinedTermSet anzsrc-for:
52 schema:name Psychology and Cognitive Sciences
53 rdf:type schema:DefinedTerm
54 anzsrc-for:1701 schema:inDefinedTermSet anzsrc-for:
55 schema:name Psychology
56 rdf:type schema:DefinedTerm
57 sg:journal.1136216 schema:issn 0010-3616
58 1432-0916
59 schema:name Communications in Mathematical Physics
60 rdf:type schema:Periodical
61 sg:person.015150461215.30 schema:affiliation https://www.grid.ac/institutes/grid.78989.37
62 schema:familyName Hepp
63 schema:givenName Klaus
64 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015150461215.30
65 rdf:type schema:Person
66 sg:pub.10.1007/bf02392399 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042147174
67 https://doi.org/10.1007/bf02392399
68 rdf:type schema:CreativeWork
69 sg:pub.10.1007/bf02526406 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054502463
70 https://doi.org/10.1007/bf02526406
71 rdf:type schema:CreativeWork
72 https://doi.org/10.1103/physrev.125.1436 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060424916
73 rdf:type schema:CreativeWork
74 https://doi.org/10.1103/physrev.75.486 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060454988
75 rdf:type schema:CreativeWork
76 https://doi.org/10.1103/physrev.80.268 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060456916
77 rdf:type schema:CreativeWork
78 https://doi.org/10.1103/physrev.82.217 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060457594
79 rdf:type schema:CreativeWork
80 https://doi.org/10.1103/revmodphys.21.434 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042535342
81 rdf:type schema:CreativeWork
82 https://www.grid.ac/institutes/grid.78989.37 schema:alternateName Institute for Advanced Study
83 schema:name The Institute for Advanced Study, Princeton, New Jersey
84 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...