Noncommutative geometry, extended (formula presented) algebra, and Grassmannian solitons in multicomponent quantum Hall systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 12, 2003, Pages

  Ezawa, Z F ^a   Tsitsishvili, G ^b   Hasebe, K ^c  

^a TOHOKU UNIVERSITY   (Japan)

^b A RAZMADZE MATHEMATICAL INSTITUTE   (Georgia)

^c Sogang University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85038338927     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.125314     Document Type: Article

References (41)

1. A. Connes, Noncommutative Geometry (Academic, New York, 1994).
2. A. Connes, M. Douglas, and A. Schwarz, JHEP9802, 003 (1998).
3. M. Douglas and C. Hull, JHEP9802, 008 (1998).
4. N. Seiberg and E. Witten, JHEP9909, 032 (1999).
5. Z.F. Ezawa, Quantum Hall Effects: Field Theoretical Approach and Related Topics (World Scientific, Singapore, 2000).
6. S M. Girvin, A H. MacDonald, and P M. Platzman, Phys. Rev. B33, 2481 (1986).
7. S. Iso, D. Karabali, and B. Sakita, Phys. Lett. B196, 143 (1992).
8. A. Cappelli, C. Trugenberger, and G. Zemba, Nucl. Phys. B396, 465 (1993).
9. Perspectives in Quantum Hall Effects, edited by S. Das Sarma and A. Pinczuk (Wiley, New York, 1997).
10. Z F. Ezawa, Phys. Rev. B55, 7771 (1997).
11. S L. Sondhi, A. Karlhede, S A. Kivelson, and E H. Rezayi, Phys. Rev. B47, 16 419 (1993).
12. S E. Barrett, G. Dabbagh, L N. Pfeiffer, K W. West, and R. Tycko, Phys. Rev. Lett.74, 5112 (1995).
13. E H. Aifer, B B. Goldberg, and D A. Broido, Phys. Rev. Lett.76, 680 (1996).
14. A. Schmeller, J P. Eisenstein, L N. Pfeiffer, and K W. West, Phys. Rev. Lett.75, 4290 (1995).
15. I B. Spielman, J P. Eisenstein, L N. Pfeiffer, and K W. West, Phys. Rev. Lett.84, 5808 (2000).
16. Z F. Ezawa and A. Iwazaki, Int. J. Mod. Phys. B6, 3205 (1992);
17. Z F. EzawaA. IwazakiPhys. Rev. B47, 7295 (1993);
18. Phys. Rev. BZ F. EzawaA. Iwazaki48, 15 189 (1993).
19. K. Moon, H. Mori, K. Yang, S M. Girvin, A H. MacDonald, L. Zheng, D. Yoshioka, and S-C. Zhang, Phys. Rev. B51, 5138 (1995).
20. K. Hasebe and Z F. Ezawa, Phys. Rev. B66, 155318 (2002).
21. H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950), especially Secs. 14 and 15 of Chap. IV.
22. M.W. Wong, Weyl Transforms (Springer-Verlag, New York, 1998).
23. M. Eliashvili and G. Tsitsishvili (unpublished).
24. S M. Girvin and T. Jach, Phys. Rev. B29, 5617 (1984).
25. Z F. Ezawa and K. Hasebe, Phys. Rev. B65, 075311 (2002).
26. J. von Neumann, Mathematical Foundation of Quantum Mechanics (Princeton University Press, Princeton, 1955), pp. 405–407.
27. A M. Perelomov, Teor. Mat. Fiz. 6, 213 (1971) [Theor. Math. Phys.6, 156 (1971)].
28. V. Bargmann, P. Butera, L. Girardello, and J R. Klauder, Rev. Math. Phys.2, 221 (1971).
29. M. Boon and J. Zak, J. Math. Phys.22, 1090 (1981).
30. Z F. Ezawa, Phys. Rev. Lett.82, 3512 (1999).
31. S M. Girvin and A H. MacDonald, Phys. Rev. Lett.58, 1252 (1987).
32. A. D’Adda, A. Luscher, and P. DiVecchia, Nucl. Phys. B146, 63 (1978).
33. A J. MacFarlane, Phys. Lett.82B, 239 (1979).
34. N. Read, Phys. Rev. Lett.62, 86 (1989).
35. N. Kumada, A. Sawada, Z F. Ezawa, S. Nagahama, H. Azuhata, K. Muraki, T. Saku, and Y. Hirayama, J. Phys. Soc. Jpn.69, 3178 (2000).
36. Y N. Joglekar and A H. MacDonald, Phys. Rev. B64, 155315 (2001).
37. J K. Jain, Phys. Rev. Lett.63, 199 (1989).
38. R B. Laughlin, Phys. Rev. Lett.50, 1395 (1983).
39. R. de Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, and D. Mahalu, Nature (London)389, 162 (1997).
40. L. Saminadayar, D C. Glattli, Y. Jin, and B. Etienne, Phys. Rev. Lett.79, 2526 (1997).
41. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).