The Bargmann-Wigner method in Galilean relativity View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1970-06

AUTHORS

C. R. Hagen

ABSTRACT

The equations of motion of a spin one particle as derived from Levy-Leblond's Galilean formulation of the Bargmann-Wigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the Bargmann-Wigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling. More generally it is demonstrated that one can replace Levy-Leblond's version of the Bargmann-Wigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the Bargmann-Wigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the Bargmann-Wigner set is found to have only a somewhat trivial counterpart in the Galilean case. More... »

PAGES

97-108

References to SciGraph publications

  • 1967-12. Nonrelativistic particles and wave equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1967-06. Galilean quantum field theories and a ghostless Lee model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01646089

    DOI

    http://dx.doi.org/10.1007/bf01646089

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1025319682


    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/2008/1103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Clinical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/11", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Medical and Health Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of Rochester", 
              "id": "https://www.grid.ac/institutes/grid.16416.34", 
              "name": [
                "Department of Physics and Astronomy, University of Rochester, Rochester, New York"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hagen", 
            "givenName": "C. R.", 
            "id": "sg:person.015442003621.64", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015442003621.64"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01646020", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006856625", 
              "https://doi.org/10.1007/bf01646020"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01646020", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006856625", 
              "https://doi.org/10.1007/bf01646020"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1073/pnas.34.5.211", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031506808"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01645427", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047586302", 
              "https://doi.org/10.1007/bf01645427"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01645427", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047586302", 
              "https://doi.org/10.1007/bf01645427"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1063/1.1724319", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057791193"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrev.139.b712", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060431306"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1103/physrev.139.b712", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1060431306"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1970-06", 
        "datePublishedReg": "1970-06-01", 
        "description": "The equations of motion of a spin one particle as derived from Levy-Leblond's Galilean formulation of the Bargmann-Wigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the Bargmann-Wigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling. More generally it is demonstrated that one can replace Levy-Leblond's version of the Bargmann-Wigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the Bargmann-Wigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the Bargmann-Wigner set is found to have only a somewhat trivial counterpart in the Galilean case.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf01646089", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136216", 
            "issn": [
              "0010-3616", 
              "1432-0916"
            ], 
            "name": "Communications in Mathematical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "18"
          }
        ], 
        "name": "The Bargmann-Wigner method in Galilean relativity", 
        "pagination": "97-108", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "789f7ef181c8392bf3ddd891bc914b267b7de091c0c3a8fc1cd22e2dee46e1e9"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf01646089"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1025319682"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf01646089", 
          "https://app.dimensions.ai/details/publication/pub.1025319682"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T09:09", 
        "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/v90/0000000338_0000000338/records_47963_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007/BF01646089"
      }
    ]
     

    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/bf01646089'

    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/bf01646089'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01646089'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01646089'


     

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

    78 TRIPLES      21 PREDICATES      32 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf01646089 schema:about anzsrc-for:11
    2 anzsrc-for:1103
    3 schema:author Nabdead82cc6c4252bfc99a52d1d584f2
    4 schema:citation sg:pub.10.1007/bf01645427
    5 sg:pub.10.1007/bf01646020
    6 https://doi.org/10.1063/1.1724319
    7 https://doi.org/10.1073/pnas.34.5.211
    8 https://doi.org/10.1103/physrev.139.b712
    9 schema:datePublished 1970-06
    10 schema:datePublishedReg 1970-06-01
    11 schema:description The equations of motion of a spin one particle as derived from Levy-Leblond's Galilean formulation of the Bargmann-Wigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the Bargmann-Wigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling. More generally it is demonstrated that one can replace Levy-Leblond's version of the Bargmann-Wigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the Bargmann-Wigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the Bargmann-Wigner set is found to have only a somewhat trivial counterpart in the Galilean case.
    12 schema:genre research_article
    13 schema:inLanguage en
    14 schema:isAccessibleForFree false
    15 schema:isPartOf Nb7ae9a54c5c746cbbc2ae1085b89bf30
    16 Nf967475492a745ada77a3df3efba970d
    17 sg:journal.1136216
    18 schema:name The Bargmann-Wigner method in Galilean relativity
    19 schema:pagination 97-108
    20 schema:productId N1a19ed1e09f1425ab7a5a6fc3917b85b
    21 Nae14ad24ef4b49038e4e718acec0497b
    22 Nf3ba55b3fccd4c2f802a6d37301a659d
    23 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025319682
    24 https://doi.org/10.1007/bf01646089
    25 schema:sdDatePublished 2019-04-11T09:09
    26 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    27 schema:sdPublisher N307710828a9744588205a40d22268b84
    28 schema:url http://link.springer.com/10.1007/BF01646089
    29 sgo:license sg:explorer/license/
    30 sgo:sdDataset articles
    31 rdf:type schema:ScholarlyArticle
    32 N1a19ed1e09f1425ab7a5a6fc3917b85b schema:name doi
    33 schema:value 10.1007/bf01646089
    34 rdf:type schema:PropertyValue
    35 N307710828a9744588205a40d22268b84 schema:name Springer Nature - SN SciGraph project
    36 rdf:type schema:Organization
    37 Nabdead82cc6c4252bfc99a52d1d584f2 rdf:first sg:person.015442003621.64
    38 rdf:rest rdf:nil
    39 Nae14ad24ef4b49038e4e718acec0497b schema:name readcube_id
    40 schema:value 789f7ef181c8392bf3ddd891bc914b267b7de091c0c3a8fc1cd22e2dee46e1e9
    41 rdf:type schema:PropertyValue
    42 Nb7ae9a54c5c746cbbc2ae1085b89bf30 schema:issueNumber 2
    43 rdf:type schema:PublicationIssue
    44 Nf3ba55b3fccd4c2f802a6d37301a659d schema:name dimensions_id
    45 schema:value pub.1025319682
    46 rdf:type schema:PropertyValue
    47 Nf967475492a745ada77a3df3efba970d schema:volumeNumber 18
    48 rdf:type schema:PublicationVolume
    49 anzsrc-for:11 schema:inDefinedTermSet anzsrc-for:
    50 schema:name Medical and Health Sciences
    51 rdf:type schema:DefinedTerm
    52 anzsrc-for:1103 schema:inDefinedTermSet anzsrc-for:
    53 schema:name Clinical Sciences
    54 rdf:type schema:DefinedTerm
    55 sg:journal.1136216 schema:issn 0010-3616
    56 1432-0916
    57 schema:name Communications in Mathematical Physics
    58 rdf:type schema:Periodical
    59 sg:person.015442003621.64 schema:affiliation https://www.grid.ac/institutes/grid.16416.34
    60 schema:familyName Hagen
    61 schema:givenName C. R.
    62 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015442003621.64
    63 rdf:type schema:Person
    64 sg:pub.10.1007/bf01645427 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047586302
    65 https://doi.org/10.1007/bf01645427
    66 rdf:type schema:CreativeWork
    67 sg:pub.10.1007/bf01646020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006856625
    68 https://doi.org/10.1007/bf01646020
    69 rdf:type schema:CreativeWork
    70 https://doi.org/10.1063/1.1724319 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057791193
    71 rdf:type schema:CreativeWork
    72 https://doi.org/10.1073/pnas.34.5.211 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031506808
    73 rdf:type schema:CreativeWork
    74 https://doi.org/10.1103/physrev.139.b712 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060431306
    75 rdf:type schema:CreativeWork
    76 https://www.grid.ac/institutes/grid.16416.34 schema:alternateName University of Rochester
    77 schema:name Department of Physics and Astronomy, University of Rochester, Rochester, New York
    78 rdf:type schema:Organization
     




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


    ...