Skip to main content
SpringerLink
Log in

Area preserving transformationsin non-commutative space and NCCS theory

  • theoretical physics
  • Published:
The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

Abstract.

We propose a heuristic rule for the area transformation on the non-commutative plane. The non-commutative area preserving transformations are quantum deformations of the classical symplectic diffeomorphisms. The area preservation condition is formulated as a field equation in the non-commutative Chern-Simons gauge theory. A higher-dimensional generalization is suggested and the corresponding algebraic structure - the infinite-dimensional sin-Lie algebra - is extracted. As an illustrative example the second-quantized formulation for electrons in the lowest Landau level is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Jackiw, Non-commuting fields and non-Abelian fluids, hep-th/0305027

  2. R. Jackiw, S.-Y. Pi, Phys. Rev. Lett. 88, 111603 (2002)

    Article  Google Scholar 

  3. R. Jackiw, S.-Y. Pi, A. Polychronakos, Ann. Phys. (NY) 301, 157 (2002)

    Article  MATH  Google Scholar 

  4. L. Susskind, The quantum Hall fluid and non-commutative Chern-Simons field theory, hep-th/0101029

  5. M. Eliashvili, G. Tsitsishvili, Int. J. Mod. Phys. B 14, 1429 (2000)

    Article  MathSciNet  Google Scholar 

  6. R.J. Szabo, Phys. Rep. 378, 207 (2003)

    Article  MATH  Google Scholar 

  7. R. Jost, Rev. Mod. Phys. 36, 572 (1964)

    Article  Google Scholar 

  8. V.I. Arnold, Mathematical methods of classical mechanics (Springer-Verlag, Berlin 1978)

  9. A.M. Perelomov, Generalized coherent states and their applications (Springer-Verlag, Berlin 1986)

  10. J. Madore, An introduction to non-commutative geometry and its physical applications (Cambridge University Press 1999),

  11. M. Eliashvili, G. Tsitsishvili, Int. J. Mod. Phys. B 16, 3725 (2002)

    Article  Google Scholar 

  12. S. Bahcall, L. Susskind, Int. J. Mod. Phys. B 5, 2735 (2002)

    Google Scholar 

  13. R. Manvelyan, R. Mkrtchyan, Phys. Lett. B 327, 47 (1994)

    Article  MathSciNet  Google Scholar 

  14. D.B. Fairlie, P. Fletcher, C.K. Zachos, Phys. Lett. B 218, 203 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  15. P. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School of Science, Yeshiva University, New York 1964)

  16. R. Jackiw, Nucl. Phys. Proc. Suppl. 108, 30 (2002)

    Article  MATH  Google Scholar 

  17. N. Seiberg, E. Witten, JHEP 9909, 032 (1999)

    Google Scholar 

  18. S. Iso, D. Karabali, B. Sakita, Phys. Lett. B 196, 142 (1992)

    Google Scholar 

  19. J. Martinez, M. Stone, Int. J. Mod. Phys. B 7, 4389 (1993)

    MathSciNet  Google Scholar 

  20. A. Cappelli, C. Trugenberger, G. Zemba, Nucl. Phys. B 396, 465 (1993)

    Article  MathSciNet  Google Scholar 

  21. Z.F. Ezawa, Quantum Hall effects (World Scientific, Singapore 2000)

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Physics, A. Razmadze Mathematical Institute, M. Aleksidze 1, 380093, Tbilisi , Georgia

    M. Eliashvili & G. Tsitsishvili

Authors
  1. M. Eliashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Tsitsishvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Eliashvili.

Additional information

Received: 13 June 2003, Revised: 11 September 2003, Published online: 7 November 2003

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eliashvili, M., Tsitsishvili, G. Area preserving transformationsin non-commutative space and NCCS theory. Eur. Phys. J. C 32, 135–140 (2003). https://doi.org/10.1140/epjc/s2003-01373-3

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2003-01373-3

Keywords

Search

Navigation