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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2010-07-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2010.060 |
| _version_ | 1818890870400745472 |
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| author | Peter A. Horváthy Luigi Martina Peter C. Stichel |
| author_facet | Peter A. Horváthy Luigi Martina Peter C. Stichel |
| author_sort | Peter A. Horváthy |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-19T17:31:47Z |
| format | Article |
| id | doaj.art-dd29afb19c6d41ff976a0162dd042067 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-19T17:31:47Z |
| publishDate | 2010-07-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-dd29afb19c6d41ff976a0162dd0420672022-12-21T20:12:26ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592010-07-016060Exotic Galilean Symmetry and Non-Commutative MechanicsPeter A. HorváthyLuigi MartinaPeter C. StichelSome 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.http://dx.doi.org/10.3842/SIGMA.2010.060noncommutative spacesGalilean symmetrydynamical systemsquantum field theory |
| spellingShingle | Peter A. Horváthy Luigi Martina Peter C. Stichel Exotic Galilean Symmetry and Non-Commutative Mechanics Symmetry, Integrability and Geometry: Methods and Applications noncommutative spaces Galilean symmetry dynamical systems quantum field theory |
| 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 |
| topic | noncommutative spaces Galilean symmetry dynamical systems quantum field theory |
| url | http://dx.doi.org/10.3842/SIGMA.2010.060 |
| work_keys_str_mv | AT peterahorvathy exoticgalileansymmetryandnoncommutativemechanics AT luigimartina exoticgalileansymmetryandnoncommutativemechanics AT petercstichel exoticgalileansymmetryandnoncommutativemechanics |