Exotic Galilean Symmetry and Non-Commutative Mechanics
Some aspects of the ''exotic'' particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minima...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146361 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Exotic Galilean Symmetry and Non-Commutative Mechanics / P.A. Horváthy, L. Martina, P.C. Stichel // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 70 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708256989773824 |
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| author | Horváthy, P.A. Martina, L. Stichel, P.C. |
| author_facet | Horváthy, P.A. Martina, L. Stichel, P.C. |
| citation_txt | Exotic Galilean Symmetry and Non-Commutative Mechanics / P.A. Horváthy, L. Martina, P.C. Stichel // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 70 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Some aspects of the ''exotic'' particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minimal as well as anomalous coupling to an external electromagnetic field is presented. Supersymmetric extension is also considered. Exotic Galilean symmetry is also found in Moyal field theory. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.
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| first_indexed | 2025-12-07T17:10:45Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146361 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:10:45Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Horváthy, P.A. Martina, L. Stichel, P.C. 2019-02-09T09:40:47Z 2019-02-09T09:40:47Z 2010 Exotic Galilean Symmetry and Non-Commutative Mechanics / P.A. Horváthy, L. Martina, P.C. Stichel // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 70 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L55; 37K65; 37L20; 83C65; 81T70 DOI:10.3842/SIGMA.2010.060 https://nasplib.isofts.kiev.ua/handle/123456789/146361 Some aspects of the ''exotic'' particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minimal as well as anomalous coupling to an external electromagnetic field is presented. Supersymmetric extension is also considered. Exotic Galilean symmetry is also found in Moyal field theory. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects. This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
 This review also includes results obtained jointly with C. Duval, Z. Horv´ath, J. Lukierski,
 M. Plyushchay and W.J. Zakrzewski, to whom we express our indebtedness. L.M. thanks the
 INFN - Sezione of Lecce for partial financial support under the project LE41. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Exotic Galilean Symmetry and Non-Commutative Mechanics Article published earlier |
| spellingShingle | Exotic Galilean Symmetry and Non-Commutative Mechanics Horváthy, P.A. Martina, L. Stichel, P.C. |
| title | Exotic Galilean Symmetry and Non-Commutative Mechanics |
| title_full | Exotic Galilean Symmetry and Non-Commutative Mechanics |
| title_fullStr | Exotic Galilean Symmetry and Non-Commutative Mechanics |
| title_full_unstemmed | Exotic Galilean Symmetry and Non-Commutative Mechanics |
| title_short | Exotic Galilean Symmetry and Non-Commutative Mechanics |
| title_sort | exotic galilean symmetry and non-commutative mechanics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146361 |
| work_keys_str_mv | AT horvathypa exoticgalileansymmetryandnoncommutativemechanics AT martinal exoticgalileansymmetryandnoncommutativemechanics AT stichelpc exoticgalileansymmetryandnoncommutativemechanics |