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SIGMA, 2010, Volume 6, 060, 26 pp. (Mi sigma517)  

This article is cited in 35 scientific papers (total in 35 papers)

Exotic Galilean Symmetry and Non-Commutative Mechanics

Peter A. Horváthya, Luigi Martinabc, Peter C. Sticheld

a Laboratoire de Mathématiques et de Physique Théorique, Universit é de Tours, Parc de Grandmont, F-37200 Tours, France
b Sezione INFN di Lecce, via Arnesano, CP. 193, I-73100 Lecce, Italy
c Dipartimento di Fisica – Università del Salento
d An der Krebskuhle 21 D-33 619 Bielefeld, Germany

Abstract: 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.

Keywords: noncommutative spaces; Galilean symmetry; dynamical systems; quantum field theory

DOI: https://doi.org/10.3842/SIGMA.2010.060

Full text: PDF file (421 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/060/
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Bibliographic databases:

ArXiv: 1002.4772
MSC: 46L55; 37K65; 37L20; 83C65; 81T70
Received: March 23, 2010; in final form July 19, 2010; Published online July 26, 2010
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Citation: Peter A. Horváthy, Luigi Martina, Peter C. Stichel, “Exotic Galilean Symmetry and Non-Commutative Mechanics”, SIGMA, 6 (2010), 060, 26 pp.

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zhang P.M., Horváthy P.A., Ngome J.-P., “Non-commutative oscillator with Kepler-type dynamical symmetry”, Phys. Lett. A, 374:42 (2010), 4275–4278  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Fedoruk S., Ivanov E., Lukierski J., “Galilean conformal mechanics from nonlinear realizations”, Phys. Rev. D, 83:8 (2011), 085013  crossref  adsnasa  isi  elib  scopus
    3. de Azcarraga J.A., Izquierdo J.M., Picon M., “Contractions of Filippov algebras”, J. Math. Phys., 52:1 (2011), 013516  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Aizawa N., Isaac Ph.S., “On irreducible representations of the exotic conformal Galilei algebra”, J. Phys. A, 44:3 (2011), 035401  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. L. Martina, “Noncommutative mechanics and exotic Galilean symmetry”, Theoret. and Math. Phys., 167:3 (2011), 816–825  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    6. Arratia O., Martin M.A., del Olmo M.A., “(2+1) Newton-Hooke Classical and Quantum Systems”, Internat J Theoret Phys, 50:7 (2011), 2035–2045  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Aizawa N., “Lowest weight representations of super Schrodinger algebras in low dimensional spacetime”, Proceedings of the 28th International Colloquium on Group-Theoretical Methods in Physics, Journal of Physics Conference Series, 284, 2011, 012007  crossref  mathscinet  isi  scopus
    8. Isidro, J.M., Fernandez De Crdoba, P., Rivera-Rebolledo, J.M., Santander, J.L.G., “Remarks on the representation theory of the Moyal plane”, Advances in Mathematical Physics, 2011, art. no. 635790  crossref  mathscinet  isi  scopus
    9. Zhang P.-M., Horvathy P.A., “Kohn condition and exotic Newton-Hooke symmetry in the non-commutative Landau problem”, Phys Lett B, 706:4–5 (2012), 442–446  crossref  mathscinet  adsnasa  isi  elib  scopus
    10. L. Martina, “Dynamics of a noncommutative monopole”, Theoret. and Math. Phys., 172:2 (2012), 1127–1135  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    11. Aizawa N., “N=2 Galilean Superconformal Algebras with a Central Extension”, J. Phys. A-Math. Theor., 45:47 (2012), 475203  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. de Melo G.R., de Montigny M., Santos E.S., “Spinless Duffin-Kemmer-Petiau Oscillator in a Galilean Non-Commutative Phase Space”, Int. J. Theor. Phys., 51:8 (2012), 2524–2539  crossref  mathscinet  zmath  isi  scopus
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    14. Martina L., “Dynamics in Non-Commutative Spaces and Generalizations”, Int. J. Geom. Methods Mod. Phys., 9:2, SI (2012), 1260012  crossref  mathscinet  isi  scopus
    15. Martina L., “Dynamics with Exotic Symmetries”, 7th International Conference on Quantum Theory and Symmetries (Qts7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012072  crossref  isi  scopus
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    17. de Melo G.R., de Montigny M., Pompeia P.J., Santos E.S., “Dirac Oscillator in a Galilean Covariant Non-Commutative Space”, Int. J. Theor. Phys., 52:2 (2013), 441–457  crossref  mathscinet  zmath  isi  scopus
    18. Henkel M., Rouhani Sh., “Logarithmic Correlators Or Responses in Non-Relativistic Analogues of Conformal Invariance”, J. Phys. A-Math. Theor., 46:49, SI (2013), 494004  crossref  mathscinet  zmath  isi  elib  scopus
    19. Abreu E.M.C. Marcial M.V. Mendes A.C.R. Oliveira W., “Analytical and Numerical Analysis of a Rotational Invariant D=2 Harmonic Oscillator in the Light of Different Noncommutative Phase-Space Configurations”, J. High Energy Phys., 2013, no. 11, 138  crossref  mathscinet  isi  scopus
    20. Ngendakumana A., Nzotungicimpaye J., Todjihounde L., “Para-Galilean Versus Galilean Noncommutative Phase Spaces”, Int. J. Geom. Methods Mod. Phys., 10:10 (2013), 1350049  crossref  mathscinet  zmath  isi  scopus
    21. Ali S.T., Bagarello F., Gazeau J.P., “Extended Pseudo-Fermions From Non Commutative Bosons”, J. Math. Phys., 54:7 (2013), 073516  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. Zhang P.M., Horvathy P.A., Andrzejewski K., Gonera J., Kosinski P., “Newton-Hooke-Type Symmetry of Anisotropic Oscillators”, Ann. Phys., 333 (2013), 335–359  crossref  mathscinet  adsnasa  isi  elib  scopus
    23. Othman, AA; De Montigny, M; Khanna, FC, “Galilean covariant Dirac equation with a Woods Saxon potential”, International Journal of Modern Physics E: Nuclear Physics, 22:12 (2013), 1350092  crossref  adsnasa  isi  scopus
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    25. Chowdhury S. Hasibul Hassan, Ali S.T., “Triply Extended Group of Translations of R-4 as Defining Group of Ncqm: Relation to Various Gauges”, J. Phys. A-Math. Theor., 47:8 (2014), 085301  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    28. Chatzistavrakidis A., “Phase Space Quantization, Noncommutativity, and the Gravitational Field”, Phys. Rev. D, 90:2 (2014), 024038  crossref  adsnasa  isi  scopus
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    31. Zhang X.-L., Sun Y.-L., Wang Q., Long Zh.-W., Jing J., “Fractional angular momentum in noncommutative generalized Chern–Simons quantum mechanics”, Eur. Phys. J. Plus, 131:7 (2016), 229  crossref  isi  elib  scopus
    32. Panella O., Roy P., “Re-Entrant Phase Transitions in Non-Commutative Quantum Mechanics”, Xxiii International Conference on Integrable Systems and Quantum Symmetries (Isqs-23), Journal of Physics Conference Series, 670, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2016, UNSP 012040  crossref  mathscinet  isi  scopus
    33. Das P., Ghosh S., “Galilei Group With Multiple Central Extension, Vorticity, and Entropy Generation: Exotic Fluid in 3+1 Dimensions”, Phys. Rev. D, 96:11 (2017), 111901  crossref  isi
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  • Symmetry, Integrability and Geometry: Methods and Applications
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