Time-space noncommutativity: quantised evolutions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2004-11-25

AUTHORS

Aiyalam P. Balachandran, Thupil R. Govindarajan, Andrey Gomes Martins, Paulo Teotonio-Sobrinho

ABSTRACT

In previous work [7], we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. [1]. Here we extend it to certain noncommutative versions of the cylinder, 3 and × S3. In all these models, only discrete time translations are possible, a result known before in the first two cases [2]–[6]. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2π/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined. More... »

PAGES

068

References to SciGraph publications

  • 1995-08. The quantum structure of spacetime at the Planck scale and quantum fields in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-05. Space-time noncommutativity, discreteness of time and unitarity in THE EUROPEAN PHYSICAL JOURNAL C
  • 2001-07. Noncommutative Manifolds, the Instanton Algebra¶and Isospectral Deformations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2004-10-30. Unitary quantum physics with time-space noncommutativity in JOURNAL OF HIGH ENERGY PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1088/1126-6708/2004/11/068

    DOI

    http://dx.doi.org/10.1088/1126-6708/2004/11/068

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1052047818


    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/2008/0101", 
            "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": "Syracuse University", 
              "id": "https://www.grid.ac/institutes/grid.264484.8", 
              "name": [
                "Department of Physics, Syracuse University, Syracuse, NY, 13244-1130, U.S.A."
              ], 
              "type": "Organization"
            }, 
            "familyName": "Balachandran", 
            "givenName": "Aiyalam P.", 
            "id": "sg:person.0675625774.88", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0675625774.88"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Institute of Mathematical Sciences", 
              "id": "https://www.grid.ac/institutes/grid.462414.1", 
              "name": [
                "The Institute of Mathematical Sciences, C. I. T. Campus Tharamani, Chennai 600 113, India"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Govindarajan", 
            "givenName": "Thupil R.", 
            "id": "sg:person.014547132667.28", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014547132667.28"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Sao Paulo", 
              "id": "https://www.grid.ac/institutes/grid.11899.38", 
              "name": [
                "Instituto de F\u00edsica, Universidade de S\u00e3o Paulo, C.P. 66318, S\u00e3o Paulo, SP, 05315-970, Brazil"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Martins", 
            "givenName": "Andrey Gomes", 
            "id": "sg:person.016134143077.03", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016134143077.03"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Sao Paulo", 
              "id": "https://www.grid.ac/institutes/grid.11899.38", 
              "name": [
                "Instituto de F\u00edsica, Universidade de S\u00e3o Paulo, C.P. 66318, S\u00e3o Paulo, SP, 05315-970, Brazil"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Teotonio-Sobrinho", 
            "givenName": "Paulo", 
            "id": "sg:person.015310735503.18", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015310735503.18"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1088/0264-9381/15/10/008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005162820"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/10/8/022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005492883"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02104515", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007206507", 
              "https://doi.org/10.1007/bf02104515"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02104515", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007206507", 
              "https://doi.org/10.1007/bf02104515"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/18/17/309", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008709043"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/13/5/018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008945779"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1088/0264-9381/14/12/015", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014989103"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(94)90207-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025485536"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0550-3213(94)90207-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025485536"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1088/1126-6708/2004/10/072", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041186034", 
              "https://doi.org/10.1088/1126-6708/2004/10/072"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0920-5632(97)00368-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044202971"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00005571", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046215769", 
              "https://doi.org/10.1007/pl00005571"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0370-2693(94)90940-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052906740"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s100520100664", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054520754", 
              "https://doi.org/10.1007/s100520100664"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2004-11-25", 
        "datePublishedReg": "2004-11-25", 
        "description": "In previous work [7], we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. [1]. Here we extend it to certain noncommutative versions of the cylinder, 3 and \u00d7 S3. In all these models, only discrete time translations are possible, a result known before in the first two cases [2]\u2013[6]. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2\u03c0/\u03b8, where \u03b8 is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2\u03c0/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1088/1126-6708/2004/11/068", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1052482", 
            "issn": [
              "1126-6708", 
              "1029-8479"
            ], 
            "name": "Journal of High Energy Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "11", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2004"
          }
        ], 
        "name": "Time-space noncommutativity: quantised evolutions", 
        "pagination": "068", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "f7ec6868f7093434f4583713dfaca7103a0370444f1213454a8cc6b1d115a79e"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1088/1126-6708/2004/11/068"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1052047818"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1088/1126-6708/2004/11/068", 
          "https://app.dimensions.ai/details/publication/pub.1052047818"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T00:44", 
        "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/v90/0000000001_0000000264/records_8697_00000275.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://iopscience.iop.org/article/10.1088/1126-6708/2004/11/068/meta"
      }
    ]
     

    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.10.1088/1126-6708/2004/11/068'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1088/1126-6708/2004/11/068'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1088/1126-6708/2004/11/068'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1088/1126-6708/2004/11/068'


     

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

    128 TRIPLES      21 PREDICATES      38 URIs      18 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1088/1126-6708/2004/11/068 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N5ffbdfd28af448a8abc6a6759ecbb0f5
    4 schema:citation sg:pub.10.1007/bf02104515
    5 sg:pub.10.1007/pl00005571
    6 sg:pub.10.1007/s100520100664
    7 sg:pub.10.1088/1126-6708/2004/10/072
    8 https://doi.org/10.1016/0370-2693(94)90940-7
    9 https://doi.org/10.1016/0550-3213(94)90207-0
    10 https://doi.org/10.1016/s0920-5632(97)00368-x
    11 https://doi.org/10.1088/0264-9381/10/8/022
    12 https://doi.org/10.1088/0264-9381/13/5/018
    13 https://doi.org/10.1088/0264-9381/14/12/015
    14 https://doi.org/10.1088/0264-9381/15/10/008
    15 https://doi.org/10.1088/0264-9381/18/17/309
    16 schema:datePublished 2004-11-25
    17 schema:datePublishedReg 2004-11-25
    18 schema:description In previous work [7], we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. [1]. Here we extend it to certain noncommutative versions of the cylinder, 3 and × S3. In all these models, only discrete time translations are possible, a result known before in the first two cases [2]–[6]. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2π/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined.
    19 schema:genre research_article
    20 schema:inLanguage en
    21 schema:isAccessibleForFree true
    22 schema:isPartOf Ncfa53625bde64c7280329b6d2a6156f3
    23 Nfae057d52e8d468ab9b9b685b7910ca4
    24 sg:journal.1052482
    25 schema:name Time-space noncommutativity: quantised evolutions
    26 schema:pagination 068
    27 schema:productId N37b6fe56fe704f27af02a9bcfa3b2f7a
    28 N5a21c35e405542b2bfc3938b9e6d6451
    29 N783aa64cccd0431cb3d8ff90cab2bc15
    30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052047818
    31 https://doi.org/10.1088/1126-6708/2004/11/068
    32 schema:sdDatePublished 2019-04-11T00:44
    33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    34 schema:sdPublisher N916478f111784a57bcb465d1ff67fce9
    35 schema:url http://iopscience.iop.org/article/10.1088/1126-6708/2004/11/068/meta
    36 sgo:license sg:explorer/license/
    37 sgo:sdDataset articles
    38 rdf:type schema:ScholarlyArticle
    39 N37b6fe56fe704f27af02a9bcfa3b2f7a schema:name readcube_id
    40 schema:value f7ec6868f7093434f4583713dfaca7103a0370444f1213454a8cc6b1d115a79e
    41 rdf:type schema:PropertyValue
    42 N5a21c35e405542b2bfc3938b9e6d6451 schema:name doi
    43 schema:value 10.1088/1126-6708/2004/11/068
    44 rdf:type schema:PropertyValue
    45 N5ffbdfd28af448a8abc6a6759ecbb0f5 rdf:first sg:person.0675625774.88
    46 rdf:rest N86a3d1ec9e9b402581f926bd4b218f5a
    47 N6dd117112db147868774040573eb086b rdf:first sg:person.015310735503.18
    48 rdf:rest rdf:nil
    49 N783aa64cccd0431cb3d8ff90cab2bc15 schema:name dimensions_id
    50 schema:value pub.1052047818
    51 rdf:type schema:PropertyValue
    52 N86a3d1ec9e9b402581f926bd4b218f5a rdf:first sg:person.014547132667.28
    53 rdf:rest Nc9d90a5eba684f58bdb2808373c38edc
    54 N916478f111784a57bcb465d1ff67fce9 schema:name Springer Nature - SN SciGraph project
    55 rdf:type schema:Organization
    56 Nc9d90a5eba684f58bdb2808373c38edc rdf:first sg:person.016134143077.03
    57 rdf:rest N6dd117112db147868774040573eb086b
    58 Ncfa53625bde64c7280329b6d2a6156f3 schema:issueNumber 11
    59 rdf:type schema:PublicationIssue
    60 Nfae057d52e8d468ab9b9b685b7910ca4 schema:volumeNumber 2004
    61 rdf:type schema:PublicationVolume
    62 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    63 schema:name Mathematical Sciences
    64 rdf:type schema:DefinedTerm
    65 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    66 schema:name Pure Mathematics
    67 rdf:type schema:DefinedTerm
    68 sg:journal.1052482 schema:issn 1029-8479
    69 1126-6708
    70 schema:name Journal of High Energy Physics
    71 rdf:type schema:Periodical
    72 sg:person.014547132667.28 schema:affiliation https://www.grid.ac/institutes/grid.462414.1
    73 schema:familyName Govindarajan
    74 schema:givenName Thupil R.
    75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014547132667.28
    76 rdf:type schema:Person
    77 sg:person.015310735503.18 schema:affiliation https://www.grid.ac/institutes/grid.11899.38
    78 schema:familyName Teotonio-Sobrinho
    79 schema:givenName Paulo
    80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015310735503.18
    81 rdf:type schema:Person
    82 sg:person.016134143077.03 schema:affiliation https://www.grid.ac/institutes/grid.11899.38
    83 schema:familyName Martins
    84 schema:givenName Andrey Gomes
    85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016134143077.03
    86 rdf:type schema:Person
    87 sg:person.0675625774.88 schema:affiliation https://www.grid.ac/institutes/grid.264484.8
    88 schema:familyName Balachandran
    89 schema:givenName Aiyalam P.
    90 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0675625774.88
    91 rdf:type schema:Person
    92 sg:pub.10.1007/bf02104515 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007206507
    93 https://doi.org/10.1007/bf02104515
    94 rdf:type schema:CreativeWork
    95 sg:pub.10.1007/pl00005571 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046215769
    96 https://doi.org/10.1007/pl00005571
    97 rdf:type schema:CreativeWork
    98 sg:pub.10.1007/s100520100664 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054520754
    99 https://doi.org/10.1007/s100520100664
    100 rdf:type schema:CreativeWork
    101 sg:pub.10.1088/1126-6708/2004/10/072 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041186034
    102 https://doi.org/10.1088/1126-6708/2004/10/072
    103 rdf:type schema:CreativeWork
    104 https://doi.org/10.1016/0370-2693(94)90940-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052906740
    105 rdf:type schema:CreativeWork
    106 https://doi.org/10.1016/0550-3213(94)90207-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025485536
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.1016/s0920-5632(97)00368-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1044202971
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1088/0264-9381/10/8/022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005492883
    111 rdf:type schema:CreativeWork
    112 https://doi.org/10.1088/0264-9381/13/5/018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008945779
    113 rdf:type schema:CreativeWork
    114 https://doi.org/10.1088/0264-9381/14/12/015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014989103
    115 rdf:type schema:CreativeWork
    116 https://doi.org/10.1088/0264-9381/15/10/008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005162820
    117 rdf:type schema:CreativeWork
    118 https://doi.org/10.1088/0264-9381/18/17/309 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008709043
    119 rdf:type schema:CreativeWork
    120 https://www.grid.ac/institutes/grid.11899.38 schema:alternateName University of Sao Paulo
    121 schema:name Instituto de Física, Universidade de São Paulo, C.P. 66318, São Paulo, SP, 05315-970, Brazil
    122 rdf:type schema:Organization
    123 https://www.grid.ac/institutes/grid.264484.8 schema:alternateName Syracuse University
    124 schema:name Department of Physics, Syracuse University, Syracuse, NY, 13244-1130, U.S.A.
    125 rdf:type schema:Organization
    126 https://www.grid.ac/institutes/grid.462414.1 schema:alternateName Institute of Mathematical Sciences
    127 schema:name The Institute of Mathematical Sciences, C. I. T. Campus Tharamani, Chennai 600 113, India
    128 rdf:type schema:Organization
     




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


    ...