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Exotic Galilean Symmetry and Non-Commutative Mechanics
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Exotic Galilean Symmetry and Non-Commutative Mechanics
Інший ID:
2010 Mathematics Subject Classification: 46L55; 37K65; 37L20; 83C65; 81T70
DOI:10.3842/SIGMA.2010.060
DOI:10.3842/SIGMA.2010.060
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
455
Завантажень:
184
Анотація:
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.
