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A mapping-independent analysis for the spectra of the non-commutative two-dimensional harmonic oscillator

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Abstract

We propose a mapping-independent method to analyze the spectra of the non-commutative two-dimensional harmonic oscillator. The path integral formulation is applied and an effective Lagrangian is obtained. The spectra are read off directly and the question of uniqueness is answered.

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References

  1. A. Connes, M. Douglas, A.S. Schwarz, J. High Energy Phys. 9802, 003 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  2. N. Seiberg, E. Witten, J. High Energy Phys. 99009, 032 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  3. M.R. Douglas, N.A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  4. C.S. Chu, P.M. Ho, Nucl. Phys. B 550, 151 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. C.S. Chu, P.M. Ho, Nucl. Phys. B 568, 447 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. F. Ardalan, H. Arfaei, M.M. Sheikh-Jabbari, Nucl. Phys. B 576, 578 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. J. Jing, Z.-W. Long, Phys. Rev. D 72, 126002 (2005)

    ADS  MathSciNet  Google Scholar 

  8. J. Jing, Phys. Rev. D 73, 086001 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  9. Z.-W. Long, J. Jing, Phys. Lett. B 560, 128 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. S. Minwalla, M. Van Raamsdonk, N. Seiberg, J. High Energy Phys. 0002, 020 (2000)

    Article  ADS  Google Scholar 

  11. M. Van Raamsdonk, N. Seiberg, J. High Energy Phys. 0003, 035 (2000)

    Article  Google Scholar 

  12. R. Gopakumar, S. Minwalla, A. Strominger, J. High Energy Phys. 0005, 020 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  13. V.P. Nair, A.P. Polychronakos, Phys. Lett. B 505, 267 (2001)

    MATH  ADS  MathSciNet  Google Scholar 

  14. B. Morariu, A.P. Polychronakos, Nucl. Phys. B 610, 531 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. D. Karabali, V.P. Nair, A.P. Polychronakos, Nucl. Phys. B 627, 565 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. B. Morariu, A.P. Polychronakos, Nucl. Phys. B 634, 326 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. J. Gamboa, M. Loewe, J.C. Rojas, Phys. Rev. D 64, 067901 (2001)

    ADS  MathSciNet  Google Scholar 

  18. J. Gamboa, M. Loewe, F. Mendez, J.C. Rojas, Mod. Phys. Lett. A 16, 2075 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. J. Gamboa, M. Loewe, F. Mendez, J.C. Rojas, Int. J. Mod. Phys. A 17, 2555 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. B. Muthukumar, P. Mitra, Phys. Rev. D 66, 027701 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  21. A. Smailagic, E. Spallucci, Phys. Rev. D 65, 107701 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  22. R.P. Feynman, Rev. Mod. Phys. 20, 367 (1948)

    Article  ADS  MathSciNet  Google Scholar 

  23. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw–Hill, New York, 1965)

    MATH  Google Scholar 

  24. H. Kleinert, Path Integral in Quantum Mechanics, Statistics and Polymer Science, 3nd edn. (World Scientific, Singapore, 2004)

    Google Scholar 

  25. C. Acatrinei, J. High Energy Phys. 0109, 007 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  26. M. Chaichian, A. Demichev, P. Presnajder, M.M. Sheikh-Jabbari, A. Tureanu, Phys. Lett. B 527, 149 (2002)

    MATH  ADS  MathSciNet  Google Scholar 

  27. M. Chaichian, A. Demichev, P. Presnajder, M.M. Sheikh-Jabbari, A. Tureanu, Nucl. Phys. B 611, 383 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. L.D. Faddeev, R. Jackiw, Phys. Rev. Lett. 60, 1692 (1988)

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China

    Jian Jing & Jian-Feng Chen

  2. Department of Physics and Electronic, School of Science, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China

    Jun-Ying Ma & Yong-Hong Guo

Authors
  1. Jian Jing
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  2. Jun-Ying Ma
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  3. Yong-Hong Guo
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  4. Jian-Feng Chen
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Correspondence to Jian Jing.

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Jing, J., Ma, JY., Guo, YH. et al. A mapping-independent analysis for the spectra of the non-commutative two-dimensional harmonic oscillator. Eur. Phys. J. C 56, 591–595 (2008). https://doi.org/10.1140/epjc/s10052-008-0682-7

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  • DOI: https://doi.org/10.1140/epjc/s10052-008-0682-7

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