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The Aharonov–Bohm effect in noncommutative quantum mechanics

  • K. Li
  • S. DulatEmail author
Theoretical Physics

Abstract

The Aharonov–Bohm effect in noncommutative (NC) quantum mechanics is studied. First, by introducing a shift for the magnetic vector potential we give the Schrödinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then, by solving the Schrödinger equations, we obtain the Aharonov–Bohm phase on NC space and NC phase space, respectively.

Keywords

Magnetic Field Field Theory Phase Space Elementary Particle Quantum Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    N. Seiberg, E. Witten, JHEP 32, 9909 (1999)Google Scholar
  2. 2.
    A. Connes, M.R. Douglas, A. Schwarz, JHEP 3, 9802 (1998); M.R. Douglas, C.M. Hull, JHEP 8, 9802 (1998)Google Scholar
  3. 3.
    F. Ardalan, H. Arfaei, M.M. Sheikh-Jabbari, JHEP 016, 9902 (1999)Google Scholar
  4. 4.
    T. Curtright, D. Fairlie, C. Zachos, Phys. Rev. D 58, 25002 (1998); L. Mezincescu, hep-th/0007046MathSciNetCrossRefADSGoogle Scholar
  5. 5.
    S.-C. Chu, P.-M. Ho, Nucl. Phys. B 550, 151 (1999); Nucl. Phys. B 568, 447 (2000)zbMATHCrossRefADSGoogle Scholar
  6. 6.
    V. Schomerus, JHEP 30, 9906 (1999)Google Scholar
  7. 7.
    G. Dunne, R. Jackiw, C. Trugenberger, Phys. Rev. D 41, 661 (1990)MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    G.G. Athanasiu, E.G. Floratos, S. Nicolis, J. Phys. A 29, 6737 (1996)zbMATHMathSciNetCrossRefADSGoogle Scholar
  9. 9.
    J. Lukierski, P.C. Stichel, W.J. Zakrzewski, Ann. Phys. 260, 224 (1997)zbMATHMathSciNetCrossRefADSGoogle Scholar
  10. 10.
    D. Bigatti, L. Susskind, Phys. Rev. D 62, 06604 (2000)MathSciNetCrossRefGoogle Scholar
  11. 11.
    J. Gamboa, M. Loeve, F. Mendez, J.C. Rojas, Mod. Phys. Lett. A 16, 2075 (2001); Phys. Rev. D 64, 067901 (2001)MathSciNetCrossRefADSGoogle Scholar
  12. 12.
    V.P. Nair, Phys. Lett. B 505, 249 (2001); V.P. Nair, A.P. Polychronakos, Phys. Lett. B 505, 267 (2001)zbMATHMathSciNetCrossRefADSGoogle Scholar
  13. 13.
    B. Morariu, A.P. Polychronakos, Nucl. Phys. B 610, 531 (2001); Nucl. Phys. B 634, 326 (2002)zbMATHMathSciNetCrossRefADSGoogle Scholar
  14. 14.
    M. Chaichian, P. Presnajder, M.M. Sheikh-Jabbari, A. Tureanu, Phys. Lett. B 527, 149 (2002); H. Falomir, J. Gamboa, M. Loeve, F. Mendez, J.C. Rojas, Phys. Rev. D 66, 045018 (2002); O.F. Dayi, A. Jellal, J. Math. Phys. 43, 4592 (2002)zbMATHMathSciNetCrossRefADSGoogle Scholar
  15. 15.
    M. Chaichian, M.M. Sheikh-Jabbari, A. Tureanu, Phys. Rev. Lett. 86, 2716 (2001); M. Chaichian, A. Demichev, P. Presnajder, M.M. Sheikh-Jabbari, A. Tureanu, Nucl. Phys. B 611, 383 (2001)CrossRefADSGoogle Scholar
  16. 16.
    B. Mirza, M. Zarei, Eur. Phys. J. C 32, 583 (2004)zbMATHMathSciNetCrossRefADSGoogle Scholar
  17. 17.
    Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)zbMATHMathSciNetCrossRefADSGoogle Scholar
  18. 18.
    R.G. Chambers, Phys. Rev. Lett. 5, 3 (1960)CrossRefADSGoogle Scholar
  19. 19.
    D. Kochan, M. Demetrian, Acta Phys. Slovaca 52, 1 (2002)Google Scholar
  20. 20.
    T. Curtright, C. Zachos, Mod. Phys. Lett. A 16, 2381 (2001); K. Bolonek, P. Kosinski, Phys. Lett. B 547, 51 (2002); K. Nozari, T. Azizi, gr-c/0504090MathSciNetCrossRefADSGoogle Scholar
  21. 21.
    S. Dulat, K. Li, hep-th/0508060Google Scholar
  22. 22.
    D. Karabali, V.P. Nair, A.P. Polychronakos, Nucl. Phys. B 627, 565 (2002)zbMATHMathSciNetCrossRefADSGoogle Scholar
  23. 23.
    R. Jengo, R. Ramachandran, JHEP 17, 0202 (2002)Google Scholar
  24. 24.
    B. Muthukumar, P. Mitra, Phys. Rev. D 66, 027701 (2002)MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    A.A. Deriglazov, Phys. Lett. B 530, 235 (2002)zbMATHMathSciNetCrossRefADSGoogle Scholar
  26. 26.
    S. Bellucci, A Nersessian, Phys. Lett. B 542, 295 (2002)zbMATHMathSciNetCrossRefADSGoogle Scholar
  27. 27.
    R. Banerjee, Mod. Phys. Lett. A 17, 631 (2002)zbMATHCrossRefADSGoogle Scholar
  28. 28.
    A.E.F. Djemai, H. Smail, Commun. Theor. Phys. 41, 837 (2004)MathSciNetGoogle Scholar
  29. 29.
    A. Kokado, Phys. Rev. D 69, 1250070 (2004)MathSciNetCrossRefGoogle Scholar
  30. 30.
    M. Demetrian, D. Kochan, hep-th/0102050; J. Zhang, Phys. Lett. B 584, 204 (2004)MathSciNetCrossRefGoogle Scholar
  31. 31.
    A. Jellal, hep-th/0105303; S. Ghosh, hep-th/0405177Google Scholar
  32. 32.
    C. Duval, P.A. Horvathy, Phys. Lett. B 479, 284 (2000); C. Duval, P.A. Horvathy, J. Phys. A 34, 10097 (2001); P. Horvathy, M. Plyushchay, JHEP 033, 0206 (2002); M.A. del Olmo, M.S. Plyushchay, hep-th/0508020; P.A. Horvathy, M.S. Plyushchay, Phys. Lett. B 595 547 (2004); Nucl. Phys. B 714, 269 (2005)zbMATHMathSciNetCrossRefADSGoogle Scholar
  33. 33.
    O. Bertolami, J.G. Rosa, C.M.L. de Aragao, P. Castorina, D. Zappala, Phys. Rev. D 72, 025010 (2005)MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    K. Li, J. Wang, C. Chen, Mod. Phys. Lett. A 20, 2165 (2005)zbMATHCrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of PhysicsHangzhou Teachers CollegeHangzhouP.R. China
  2. 2.Department of PhysicsXinjiang UniversityUrumqiP.R. China
  3. 3.The Abdus Salam International Center for Theoretical PhysicsTriesteItaly

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